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AD-A171  371 


UNCLASSIFIED 


EFFECT  OF  DRAIN  SIZE  ON  THE  INTERNAL  FRACTURINS  OF 
POLVCRVSTALLINE  ICE(U>  COLD  REGIONS  RESEARCH  AND 
ENGINEERING  LAB  HANOVER  NH  D  H  COLE  JUL  86  CRREL-86-5 


_ Unclassified _ 

SECURITY  CLASSIFICATION  OF  THIS  PAGE  (When  Dote  Entered) 

REPORT  DOCUMENTATION  PAGE  \  be^cSSJEetoStorm 

r  REPOST  NUMBER  |2.  GOVT  ACCESSION  NO.  '  RECIPIENT'S  CATALOG  NUMBER 


1.  REPORT  NUMBER 


CRREL  Report  86-5 


t>  -4  in  i  Wn  I 


A.  Title  (and  Submit)  ! 

EFFECT  OF  GRAIN  SIZE  ON  THE  INTERNAL  FRACTURING 
OF  POLYCRYSTALLINE  ICE 


[7T  author?  «; 


David  M.  Cole 


9.  PERFORMING  ORGANIZATION  NAME  AND  ADDRESS 

U.S.  Army  Cold  Regions  Research  and  Engineering  Laboratory 
Hanover,  bfew  Hampshire  03755-1290 


It.  CONTROLLING  OFFICE  NAME  AND  ADDRESS 


'  type  OF  REPORT  A  PERIOD  COVERED 


6.  PERFORMING  ORG.  REPORT  NUMBER 


8.  CONTRACT  OR  GRANT  NUMBER?*! 


10.  PROGRAM  ELEMENT,  PROJECT,  TASK 
AREA  &  WORK  UNIT  NUMBERS 


Office  of  the  Chief  of  Engineers 
Washington,  DC  20314-1000 


DA  Project  4A762730AT42 
Task  A,  Work  Unit  004 

12.  REPORT  DATE 

July  1986 

13.  NUMBER  OF  PAGES 


W.  MONITORING  AGENCY  NAME  8  ADORESS?//  dlllerent  Irom  Controlling  Olllce)  i  '5.  SEC  U  Rl  T  Y  CL  ASS.  (ol  thle  report) 

!  Unclassified 


IS*.  DECLASSIFICATION  DOWNGRADING 
SCHEDULE 


I  16-  DISTRIBUTION  STATEMENT  (ol  tl tie  Report! 


Approved  for  public  release;  distribution  is  unlimited. 


[17.  DISTRIBUTION  STATEMENT  (ol  the  abetract  entered  In  Block  20,  II  dllfarant  Irom  Report) 


IS.  SUPPLEMENTARY  NOTES 


1 19.  KEY  WORDS  (Continue  on  ravaraa  alda  II  nacaaaary  and  Identity  by  block  number) 


Acoustic  emissions 
Creep  tests 
Fracture  (mechanics) 
Grain  size 


Ice 

Polycrystalline 


rr 


20.  ABSTRACT  (XTeotfnue  ms  fewer  me  If  nmceomory  end  Identity  by  block  number) 

^This  work  presents  the  results  of  a  study  to  examine  the  effects  of  grain  size  on  the  number  and  size  of  internal  micro¬ 
fractures  in  ^olycrystalline  ice.  Laboratory-prepared  specimens  were  tested  under  uniaxial,  constant-load  creep  con¬ 
ditions  at  -5bC.  Grain  size  ranged  from  1 .5  to  6.0  mm.  This  range  of  grain  size,  under  an  initial  creep  stress  of  2.0 
MPa,  led  to  a  significant  change  in  the  character  of  deformation.  The  finest-grained  material  displayed  no  internal 
cracking  and  typically  experienced  strains  of  10’*  at  the  minimum  creep  rate  4min ,  The  coarse-grained  material  ex¬ 
perienced  severe  cracking  and  a  drop  in  the  strain  at  cmin  to  approximately  4s?  10‘3 .  Extensive  post-test  optical  analy¬ 
sis  allowed  estimation  of  the  size  distribution  and  number  of  microcracks  in  the  tested  material.  These  data  led  to 
the  development  of  a  relationship  between  the  average  crack  size  and  the  average  grain  size.  Additionally,  the  crack 

00  ,  j2Tt3  1473  edition  OF  I  MOV  .*  is  obsolete  Unclassified 

.  SECURITY  CLASSIFICATION  of  THIS  PAGE  (When  Data  Entered) 


vVvv.’‘. 


WtTI 


•\V  l/.v  v  / 


20.  Abstract  (cont’d). 

.  size  distribution,  when  normalized  to  the  grain  diameter,  was  very  similar  for  all  specimens  tested.  The  results  indi¬ 
cate  that  the  average  crack  size  is  approximately  one-half  the  average  grain  diameter  over  the  stated  grain  size 
range.  A  dislocation  pileup  model  is  found  to  adequately  predict  the  onset  of  internal  cracking.  The  work  em¬ 
ployed  acoustic  emission  techniques  to  monitor  the  fracturing  activity.  This  information  shed  light  on  the  time 
and  strain  at  which  the  fracturing  began  and  when  the  peak  fracturing  rate  occurred.  Other  topics  covered  in  this 
report  include  creep  behavior,  crack  healing,  the  effect  of  stress  level  on  fracture  size  and  the  orientation  of  cracked 
grains.  Theoretical  aspects  of  the  grain  size  effect  on  material  behavior  are  also  given. 


PREFACE 


This  report  was  prepared  by  David  M.  Cole,  Research  Civil  Engineer,  of  the  Applied  Re¬ 
search  Branch,  Experimental  Engineering  Division,  U.S.  Army  Cold  Regions  Research  and 
Engineering  Laboratory.  Funding  for  this  research  was  provided  by  DA  Project  4A762730 
AT42,  Research  in  Snow,  Ice  and  Frozen  Ground,  Task  A,  Properties  of  Cold  Regions 
Materials,  Work  Unit  004,  Strength  Characteristics  of  Ice  and  Frozen  Ground. 

The  author  would  like  to  express  his  appreciation  to  Dr.  Erland  Schulson  for  his  help  and 
support  in  the  research  described  in  this  report.  He  also  thanks  Dr.  Samuel  Colbeck,  Stephen 
Ackley,  and  Dr.  Harold  Frost  for  their  help  and  useful  suggestions,  and  for  their  technical 
review  of  this  report. 

The  author  is  indebted  to  many  members  of  the  CRREL  staff  for  their  support  in  various 
aspects  of  this  work.  In  particular,  thanks  are  given  to  Dr.  Ronald  Liston  for  his  encourage¬ 
ment  throughout  this  program,  and  to  Dr.  Anthony  Gow  for  many  helpful  suggestions. 
Special  thanks  are  given  to  Gary  Decoff  for  invaluable  help  in  the  computer  aspects  of  this 
work,  Nancy  Richardson  for  her  tireless  efforts  in  typing  the  manuscript  and  Matthew  Pacil- 
lo  for  drafting  the  illustrations. 


/  “■'f'r'OU:,c ed  * 

LZf^ton  L 

/  ..  ~~ 

'b^tionj . — 

0,5t  /  A^'J 


■w'-* 


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i 


CONTENTS 


Page 


Abstract .  i 

Preface .  iii 

Background .  1 

Present  research  in  perspective .  2 

Explanations  of  the  grain-size  dependency .  2 

Grain  size  effects  on  the  ductile  to  brittle  transition .  3 

Nucleation  mechanisms  and  modeling .  4 

Characteristic  size  of  nucleated  crack .  6 

Cracking  in  ice .  8 

Detection  of  internal  fracturing  by  acoustic  emission  techniques .  10 

Test  methods .  12 

Specimen  preparation .  12 

Creep  testing  apparatus .  12 

Crack  length  and  crack  density  measurements .  13 

Crack  healing  measurements .  14 

Thin  section  photographs .  14 

Grain  size  determination .  14 

Acquisition  of  acoustic  emission  data .  16 

Presentation  of  results .  18 

Specimen  characteristics .  18 

Microcrack  measurements .  18 

Creep  behavior .  22 

Crack  healing .  26 

Slip  plane  length  distribution .  27 

Acoustic  emission  observations .  27 

Grain  orientation .  28 

Analysis  and  discussion .  33 

Thick  section  observations .  34 

The  grain  size  vs  crack  size  relationship .  35 

Crack  nucleation  condition .  38 

Crack  density  and  specimen  strain .  40 

Creep  behavior .  40 

Normalized  crack  length .  43 

Location  of  cracks .  44 

Acoustic  emission  activity . .  45 

Summary  and  conclusions .  48 

Suggestions  for  future  work .  48 

Literature  cited .  49 

Appendix  A:  Crack  length  histograms .  53 

Appendix  B:  Crystal  orientations .  71 


ILLUSTRATIONS 

Figure 

1.  Stress/grain-size  relationship  showing  transition  grain  size  for  ductile  to  brittle 

behavior . 

2.  Most  favorable  crack  orientation . 

3.  Typical  untested  specimen . 

4.  Creep  testing  apparatus  showing  displacement  transducer  and  mounting  clamps 

on  specimen . 

5.  Schematic  showing  typical  locations  of  thick  sections  in  the  cylindrical  ice  speci¬ 

mens  . 

6.  Typical  thin  sections  of  test  material .  . 

7.  AE  transducer  mounted  on  specimen . 

8.  Idealized  acoustic  emission  waveforms . 

9.  Typical  crack  length  histogram . 

10.  Mean  crack  length  vs  mean  grain  diameter . 

1 1 .  Mosaics  formed  from  enlarged  thick  section  photographs . 

12.  Crack  density  vs  grain  diameter . 

13.  Crack  density  vs  axial  strain  for  several  ranges  in  grain  size . 

14.  Strain-time  plots  for  several  tests . 

15.  Creep  curves  for  all  tests . 

16.  Minimum  creep  rate  vs  grain  diameter . 

17.  Strain  at  minimum  creep  rate  vs  grain  diameter  for  10  specimens . 

18.  Time-lapse  photographs  of  crack  healing,  face  view . 

19.  Time-lapse  photographs  of  crack  healing,  edge  view . 

20.  Crack  length  vs  time . 

21.  Slip  plane  length  distribution . 

22.  Typical  acoustic  emission  data . 

23.  Acoustic  emission  rate  data . 

24.  Thick  section  photograph  taken  parallel  to  the  axis  of  applied  stress . 

25.  Distribution  of  the  angle  between  the  axis  of  compressive  stress  and  the  plane  of 

the  observed  crack . 

26.  Theoretical  prediction  and  observed  relationship  for  the  average  crack  size/ 

grain  size  relationship . 

27.  Creep  curve  for  a  fine-grained  specimen  under  high  load . 

28.  The  effect  of  grain  growth  on  grain  size . 

29.  Normalized  fracture  length  distribution  for  all  tests . 

30.  Maximum  normalized  crack  length  vs  grain  diameter  for  all  tests . 

3 1 .  Normalized  crack  length  histograms . 

32.  Mean  AE  amplitude  vs  mean  crack  length . 


TABLES 

Table 

1.  Creep  data . 

2.  Grain  size  estimates  and  seed  grain  sizes . . . 

3.  Crack  location . 

4.  Results  of  microfracture  observations. . . . 

5.  Results  of  acoustic  emission  observations. 


W 


EFFECT  OF  GRAIN  SIZE  ON  THE  INTERNAL 
FRACTURING  OF  POLYCRYSTALLINE  ICE 

David  M.  Cole 


Ice  exhibits  brittle  behavior  at  high  tempera¬ 
tures  under  a  variety  of  loading  conditions.  A  key 
factor  causing  this  brittleness  is  the  lack  of  a  suffi¬ 
cient  number  of  independent  slip  systems;  five  are 
required  to  satisfy  the  von  Mises  criterion  for  an 
arbitrary  change  in  shape.  Slip  is  likely  on  the 
basal  and  prismatic  planes  (Goodman  1977),  but 
these  do  not  provide  the  needed  five  systems.  So, 
given  the  inability  of  the  lattice  to  accommodate 
plastic  deformation  by  slip  alone,  and  given  a 
loading  condition  sufficiently  rapid  to  prevent  dif- 
fusional  mechanisms  from  operating  effectively, 
ice  will  develop  cracks.  The  size  and  extent  of  the 
tracks  at  a  given  temperature  depend  on  the  ap¬ 
plied  stress  and  structural  characteristics  of  the 
polycrystalline  aggregate,  such  as  the  orientation, 
shape  and  size  of  the  grains.  Microstructural  dif¬ 
ferences  such  as  those  between  freshwater  ice  and 
sea  ice  also  influence  cracking  activity. 

The  internal  shear  stress  generated  during  either 
tensile  or  compressive  loading  nucleates  cracks. 
Under  certain  conditions,  these  cracks  propagate 
only  a  short  distance  before  coming  to  rest  within 
the  material.  Given  sufficiently  high  stress  levels, 
the  cracks  thus  nucleated  can  propagate  through 
the  material  to  cause  brittle  fracture. 

The  nuclcation  of  stable,  non-propagating 
cracks  is  of  interest  for  a  number  of  reasons. 
These  cracks  are  the  flaws  that  can  propagate 
under  subsequent  tensile  loading.  In  compression, 


when  the  cracks  do  not  propagate,  they  are  re¬ 
sponsible  for  the  gradual  weakening  of  the  struc¬ 
ture  as  straining  proceeds.  Gold  (1970)  noted  that 
ice  passes  directly  from  primary  to  tertiary  creep 
as  a  result  of  the  structural  damage  caused  by  in¬ 
ternal  cracking. 

This  report  concentrates  on  the  effect  of  grain 
size  on  the  internal  cracking  of  polycrystalline  ice 
with  equiaxed  grains.  Relatively  little  research  has 
been  done  in  this  area,  although  considerable 
work  exists  on  the  cracking  of  columnar  grained 
ice,  and  such  work  is  examined  in  detail.  Addi¬ 
tionally,  some  relevant  contributions  regarding 
cracking  in  materials  other  than  ice  are  covered. 

Initial  discussions  center  on  the  root  of  the 
grain-size  dependency  in  material  behavior.  The 
effect  of  grain  size  on  the  ductile/brittle  nature  of 
deformation  is  then  addressed.  Subsequent  sec¬ 
tions  give  attention  to  crack  nucleation  mechan¬ 
isms  and  the  cracking  activity  observed  in  ice.  The 
final  sections  describe  acoustic  emission  tech¬ 
niques  for  crack  detection  and  their  application  to 
the  field  of  ice  mechanics. 


BACKGROUND 

This  work  primarily  examines  the  dislocation 
pileup  mechanism  for  crack  nucleation.  While  the 
operation  of  a  mechanism  based  on  stress  concen- 


trations  arising  from  grain  anisotropy  is  recog¬ 
nized,  it  is  felt  that  the  pileup  mechanism  will 
dominate  at  the  strain  rates  and  temperatures  in¬ 
vestigated  in  this  work. 

Present  research  in  perspective 

The  role  of  grain  boundaries  in  crack  formation 
has  long  been  recognized.  However,  very  little  has 
been  done  to  quantify  the  relationship  between 
grain  size  and  crack  size,  primarily  due  to  the  dif¬ 
ficulty  in  making  the  appropriate  observations  in 
most  materials. 

A  primary  objective  of  this  research  was  to  de¬ 
velop  a  crack  size/grain  size  relationship  for  ice. 
Because  of  its  optical  properties  and  its  propensity 
to  develop  cracks  under  conditions  of  practical 
concern,  polycrystalline  ice  was  ideally  suited  to 
such  a  study  of  internal  cracking  activity.  The  op¬ 
tical  techniques  employed  allow  the  estimation  of 
the  crack  size  distribution  as  well  as  the  number  of 
cracks  per  unit  volume  in  the  tested  material. 

Another  objective  was  to  demonstrate  the  effect 
of  grain  size  relative  to  the  onset  of  internal  crack¬ 
ing.  As  noted  above,  earlier  work  clearly  demon¬ 
strated  the  influence  of  stress  or  strain  rate  on  the 
tendency  of  ice  to  develop  cracks,  but  the  influ¬ 
ence  of  grain  size  alone  in  this  regard  has  not  been 
clearly  demonstrated.  This  objective  was  accom¬ 
plished  by  monitoring  the  extent  of  cracking  in 
specimens  of  increasing  grain  size  while  such  vari¬ 
ables  as  stress,  temperature  and  the  amount  of 
strain  were  held  constant.  The  conditions  for  the 
onset  of  cracking  were  analyzed  in  terms  of  estab¬ 
lished  crack  nucleation  theory. 

Additionally,  this  research  addressed  several 
peripheral  topics  germane  to  the  experimental 
methods  employed  and  to  the  mechanical  proper¬ 
ties  of  ice  in  general.  These  topics  included  the  ob¬ 
servation  of  microcracks  at  various  times  after 
formation  to  monitor  shape  change  (the  crack 
healing  process),  an  examination  of  the  effect  of 
grain  size  on  creep  behavior,  acoustic  emissions 
activity,  and  observations  on  the  orientation  of 
grains  containing  cracks  and  the  orientation  of  the 
cracks  themselves  relative  to  the  axis  of  compres¬ 
sive  stress. 

The  information  obtained  by  the  accomplish¬ 
ment  of  these  objectives  will  be  useful  in  several 
respects.  The  crack  size/grain  size  relationships 
will  enhance  our  understanding  of  the  effect  of 
grain  size  on  the  fracture  strength  of  unflawed  ice. 
Knowledge  of  the  size  distribution  and  number  of 
cracks  will  allow  a  more  precise  examination  of 
the  effects  of  stress/strain  history  on  the  mechani¬ 


cal  properties  of  the  material.  Verification  of  the 
crack  nucleation  model  will  allow  its  application 
with  greater  confidence. 

The  crack  healing  observations  will  be  useful  in 
that  the  results  indicate  the  change  in  crack  geom¬ 
etry  with  time.  This  makes  it  possible  to  assess  the 
period  for  which  a  newly  formed  crack  is  a  signifi¬ 
cant  source  of  internal  stress  concentration. 

Explanations  of  the  grain-size  dependency 

Armstrong  (1979)  pointed  out  the  broad  applic¬ 
ability  of  the  Hall-Petch  relationship  between 
strength  and  grain  size: 

a  =  oo+Kd (1) 

where  a  =  stress 

o9  =  frictional  stress 
K  -  Hall-Petch  slope 
d  =  grain  diameter. 

He  summarized  results  demonstrating  the  validity 
of  the  Hall-Petch  relationship  for  tensile  yield  and 
brittle  fracture  stresses  and  for  the  flow  stress  at 
various  levels  of  strain.  Equation  1  is  essentially 
an  empirical  relationship  and  much  work  has  been 
carried  out  in  efforts  to  develop  a  firm  theoretical 
basis  for  its  veracity. 

Li  and  Chou  (1970)  review  the  major  theoretical 
arguments  that  have  been  put  forth  to  explain  the 
d "  dependency.  Early  work  (see  Stroh  1957  for  a 
useful  summary)  led  to  the  wide  acceptance  of  a 
dislocation  pileup  model  to  explain  the  observed 
grain  size  dependency.  Direct  observations  of  dis¬ 
location  pileups  at  grain  boundaries  made  a  very 
convincing  case  for  this.  Arguments  for  the  dislo¬ 
cation  pileup  model  are  based  on  the  supposition 
that  shear  deformation  passes  from  grain  to  grain 
when  dislocations,  acting  under  an  imposed  stress, 
pile  up  at  a  grain  boundary  and  produce  a  stress 
concentration  that  is  capable  of  producing  slip  in 
the  adjacent  grain. 

A  pileup  at  the  edge  of  one  grain  of  diameter  d 
induces  a  shear  stress  t  at  a  distance  r  in  the  adja¬ 
cent  grain  according  to  the  relationship 

r  =  r,(d/r)v‘  (2) 

where  r,  is  the  applied  shear  stress.  Given  that  a 
stress  is  required  to  generate  slip  in  the  adjacent 
grain,  and  that  a  frictional  stress  r,  must  be  over¬ 
come,  eq  2  may  be  rewritten: 

Tj  =  (rf-  r,)(cf/r)w.  (3) 


2 


Solving  for  the  applied  shear  stress, 

r.  =  T,  +  ri(r/d)v'.  (4) 

Thus  arises  the  d  *  dependency  according  to  the 
dislocation  pileup  mechanism. 

Interestingly,  as  Li  and  Chou  (1970)  pointed 
out,  materials  in  which  no  pileups  are  observed 
have  been  found  to  obey  the  Hall-Petch  relation¬ 
ship.  This  has  led  to  a  search  for  alternative  ex¬ 
planations  of  the  observed  stress/grain-size  rela¬ 
tionship,  namely  work  hardening  and  grain  boun¬ 
dary  source  theories. 

The  work  hardening  theory  derives  arf'“  de¬ 
pendency  by  using  the  experimentally  established 
fact  that  the  yield  or  flow  stress  is  a  function  of  the 
square  root  of  the  dislocation  density,  q: 

a  =  <Jo  +  Ctflb>J^Q  (5) 

whjre  a  =  a  numerical  constant 

o„  =  the  ordinate  intercept  in  a  plot  of  a  vs 
cf* 

n  =  the  shear  modulus 
b  =  the  Burgers  vector. 

Other  experimental  observations  indicate  that  the 
dislocation  density  at  yield  varies  inversely  with 
grain  size,  thus  explaining  the  d*  dependency. 

The  grain  boundary  source  theory  considers 
grain  boundaries  capable  of  generating  disloca¬ 
tions.  The  length  of  the  dislocation  lines  generated 
in  this  manner  is  directly  proportional  to  the  grain 
boundary  area.  When  this  is  normalized  to  grain 
volume  to  give  a  dislocation  density,  a  ct'  depen¬ 
dency  arises.  Substitution  into  eq  5  again  yields 
the  <t *  dependency. 

Stroh’s  (1957)  work  developed  a  crack  nuclea- 
tion  model  based  on  the  dislocation  pileup  mecha¬ 
nism.  In  order  to  proceed  with  complete  confi¬ 
dence  in  the  use  of  such  a  model,  direct  evidence 
of  dislocation  pileups  in  the  material  in  question 
would  be  necessary.  Sinha  (1978)  presented  photo¬ 
graphic  evidence  of  dislocations  in  polycrystalline 
ice.  Using  an  etching  and  replication  technique,  he 
demonstrated  the  existence  of  dislocation  pileups 
at  grain  boundaries  through  the  observation  of 
etch-pits  on  carefully  prepared  surfaces.  Further¬ 
more,  Sinha’s  results  clearly  indicated  the  glide  of 
basal  dislocations  under  an  applied  stress.  He 
noted  the  appearance  of  dislocations  on  the  f  1 120) 
surface  parallel  to  the  basal  plane.  However,  work 
by  Gold  (1972)  indicates  that  the  pileup  mecha¬ 


nism  may  not  be  the  only  one  to  cause  cracking  in 
ice. 

Gold  (1972)  demonstrated  that  two  independent 
crack  distributions  exist  in  columnar-grained  ice. 
One  was  strain-dependent  and  was  consistent  with 
a  dislocation  pileup  mechanism.  The  other  ap¬ 
peared  to  be  essentially  independent  of  strain,  was 
mainly  composed  of  grain  boundary  cracks  and 
represented  approximately  24%  of  the  total  crack 
population.  Gold  (1972)  speculated  that  cracking 
represented  by  the  latter  distribution  dominated  at 
high  rates  of  loading,  thus  associating  grain  boun¬ 
dary  cracking  with  brittle  behavior.  Furthermore, 
he  suggested  that  the  balance  between  these  two 
crack  distributions  determines  the  transition  from 
ductile  to  brittle  behavior  in  compression. 

The  mechanism  of  this  strain-independent  crack 
distribution  is  not  clear  but  appears  to  be  more 
closely  associated  with  elastic  behavior  than  with 
piastic  behavior.  If  this  is  indeed  the  case,  the  pile¬ 
up  mechanism  should  be  adequate  when  signifi¬ 
cant  plastic  flow  occurs.  However,  its  applicability 
is  liable  to  diminish  as  behavior  becomes  more 
brittle. 

It  is  very  difficult  to  discern  the  crack  nuclea- 
tion  mechanism  from  gross  specimen  observa¬ 
tions.  As  Stroh  (1957)  pointed  out,  the  dislocation 
pileup  model  predicts  the  likelihood  of  cracking  at 
strains  on  the  order  of  those  expected  for  cracks 
caused  by  elastically  generated  stress  concentra¬ 
tions. 

In  light  of  the  above,  while  the  dislocation  pile¬ 
up  mechanism  may  not  be  the  only  source  of  stress 
concentrations  of  sufficient  magnitude  to  generate 
cracks,  it  reflects  the  bulk  of  the  cracking  activity 
of  ice  when  the  behavior  is  not  purely  brittle. 

Grain  size  effects  on  the 
ductile  to  brittle  transition 

Through  its  influence  over  the  internal  distribu¬ 
tions  of  stress,  grain  size  exerts  a  significant  influ¬ 
ence  over  many  aspects  of  material  behavior. 
Most  germane  to  the  present  work  is  the  influence 
of  grain  size  on  the  ductile/brittle  character  of  de¬ 
formation. 

Armstrong  (1970)  explained  the  effect  of  grain 
size  on  the  ductile-to-brittle  transition  in  mild 
steel.  Due  to  the  thermal  effects  on  the  stress  re¬ 
quired  to  cause  either  yielding  or  fracture,  the  fail¬ 
ure  stress  generally  increases  as  temperature  de¬ 
creases.  At  a  constant  strain  rate,  the  material 
undergoes  a  transition  from  ductile  to  brittle  be¬ 
havior  at  some  temperature  Tc.  An  increase  in 


grain  size  lowers  the  peak  stress  experienced  under 
constant  strain  rate  and  increases  Tc.  The  drop  in 
peak  stress  follows  the  slope  of  the  Hall-Petch  re¬ 
lationship.  The  rise  in  Te  results  from  the  relation¬ 
ship  between  grain  size  and  the  temperature- 
dependent  frictional  stress  term  of  the  Hall-Petch 
relationship,  a,. 

At  constant  temperature  and  strain  rate  a  criti¬ 
cal  grain  size  may  be  determined  above  which  the 
material  is  brittle  and  below  which  the  material  is 
ductile.  Stroh  (1957)  arrived  at  a  relationship  be¬ 
tween  transition  temperature  and  grain  size  by  us¬ 
ing  a  stochastic  method: 

1  /  Tc  =  -  V,  (k/u)  log(d)  +  c  (6) 

where  T,  =  transition  temperature 
k  =  Boltzmann  constant 
c  =  a  constant  independent  of  tempera¬ 
ture  and  strain  rate 
u  =  activation  energy. 

More  recently,  Schulson  (1979)  derived  a  relation¬ 
ship  for  the  tensile  case  between  the  critical  grain 
size  and  material  characteristics  of  the  form 

* .  a. 

where  K,c  is  the  critical  stress  intensity  factor.  This 
expression  stems  from  the  fact  that,  at  some  par¬ 
ticular  grain  size,  both  slip-propagation  controlled 
yield  (ductile  behavior)  and  crack-nudeation  con¬ 
trolled  fracture  (brittle  behavior)  are  equally  like¬ 
ly.  Figure  1  shows  the  stress  vs  grain  size  curves 
for  the  ductile  and  brittle  cases.  The  intersection 
defines  the  critical  grain  size.  In  the  present  work, 
grain  size  varies  about  the  critical  grain  size  and 
the  resulting  material  behavior  changes  in  charac¬ 
ter  accordingly. 

The  relationship  between  grain  size  and  7V  can 
be  seen  in  Figure  1 .  A  lower  Te  results  from  a  high¬ 
er  value  of  a.  in  the  Hall-Petch  expression  describ¬ 
ing  curve  I.  This  has  the  effect  of  raising  curve  la 
in  Figure  1  to  curve  lb  and  thus  shifting  the  in¬ 
tercept  with  curve  2  to  a  lower  grain  size.  The  ex¬ 
pression  for  curve  2  is  much  less  sensitive  to  tem¬ 
perature  variations.  Consequently,  it  does  not 
shift  appreciably  and  the  effect  of  temperature  on 
the  point  of  intersection  is  not  significantly  dimin¬ 
ished. 

An  increase  in  grain  size  over  the  critical  value 
brings  about  the  reduction  in  overall  specimen 
strain  prior  to  fracture  often  associated  with  in¬ 
creased  brittleness.  Results  given  by  Mendiratta  et 


© 


Figure  l.  Stress  /grain  size  relationship  showing 
transition  grain  size  for  ductile  (curve  2)  to  brittle 
(curves  la  and  lb)  behavior.  Shift  from  curve  la  to 
lb  shows  effect  of  decreasing  temperature  on  a,  and  on 
the  critical  grain  size. 


al.  (1976)  show  a  reduction  in  strain  to  fracture  in 
a  titanium  alloy  from  0.21  to  0.02  arising  only 
from  an  increase  in  grain  size.  For  this  change  to 
take  place,  grain  size  was  increased  an  order  of 
magnitude  from  9  to  90  #tm,  and  the  fracture  mode 
changed  from  ductile  dimple  to  brittle  cleavage. 

According  to  work  by  Terlinde  and  Luetjering 
(1982)  grain  size  exerted  an  influence  on  fracture 
strain  of  the  form 

efad-'.  (8) 

In  this  work,  as  in  the  abovementioned  results  of 
Mendiratta  et  al.  (1976),  a  reduction  in  grain  size 
changed  the  behavior  of  a  titanium-aluminum  al¬ 
loy  from  primarily  brittle  to  primarily  ductile, 
with  a  significant  increase  in  failure  strain. 

Nudeation  mechanisms  and  modeling 

Most  current  thought  on  crack  nucleation  stems 
from  a  model  given  by  Zener  (1948).  According  to 
this  model  a  crack  nucleates  when  the  normal 
stress  generated  by  a  dislocation  pileup  reaches  a 
critical  level;  this  causes  the  material  to  fracture 
and  allows  the  dislocations  to  coalesce,  relieving 
the  local  strain  energy.  A  relatively  strong  barrier 
must  be  present  in  order  for  the  pileup  to  build  to 
a  sufficient  stress  to  nucleate  the  crack.  Lattice 
orientation  changes  at  grain  boundaries  or  hard 
inclusions  may  serve  as  effective  barriers. 

Stroh  (1957)  presented  an  extensive  analysis  of 
the  stresses  required  to  nucleate  a  crack.  Stroh 
based  his  development  on  the  concept  of  a  disloca- 


4 


^  .v 


tion  pileup  on  a  slip  plane,  acted  upon  by  a  shear 
stress,  which  generates  a  sufficient  normal  stress 
in  a  neighboring  grain  to  produce  a  cleavage  frac¬ 
ture.  He  derived  the  expression 

oi  =  3  ir-yAt/8  (1  -v)(  (9) 

for  the  resolved  shear  stress  on  the  slip  plane  and, 

by  using 

f  =  nbn/ir  (1  —  v)a,  (10) 

showed  the  nucleation  condition  to  be 


nocb  =  V,  T2y 


(11) 


where  oc 

y 

V 

( 

b 

n 


resolved  effective  shear  stress  on  the 

slip  plane 

surface  energy 

shear  modulus 

Poisson’s  ratio 

length  of  pileup 

the  Burgers  vector 

number  of  dislocations  in  the  pileup. 


In  eq  9,  coefficients  have  been  determined  for  the 
case  of  the  crack  forming  at  an  orientation  to  the 
slip  plane  which  maximizes  the  stress  on  the  form¬ 
ing  crack.  Stroh  determined  this  angle  to  be  70.5 
He  also  points  out  that  a  crack  length  term  does 
not  appear  in  this  expression. 

In  a  later  work.  Smith  and  Barnby  (1967)  re¬ 
formulated  Stroh’s  approach  to  account  for  the 
effect  of  shear  stress  on  the  nucleation  process  and 
developed  orientation  factors  to  account  for 
geometries  other  than  Stroh’s  case  of  maximum 
normal  stress. 

Smith  and  Barnby  (1967)  give  the  nucleation 
condition  for  a  pileup  of  edge  dislocations  of  a 
single  sign  as 


where  F[<t>)  =  (5  +  2cos <t>  -  3cos20)/4  and  the 
corresponding  number  of  dislocations  required 
under  a,  is 


n 


T!y  1 

2afb  F\<t>) 


(13) 


alysis,  the  crack  length  does  not  appear  in  the  nu¬ 
cleation  criterion,  only  the  pileup  length. 

The  fact  that  the  nucleation  condition  does  not 
contain  a  crack  length  term  is  a  key  point.  The 
length  of  the  crack  is  determined  by  both  the  nor¬ 
mal  stress  component  and  the  presence  of  obsta¬ 
cles  to  its  growth  such  as  grain  boundaries.  In 
other  words,  once  the  separation  of  atom  planes  is 
initiated,  it  will  continue  as  long  as  sufficient  nor¬ 
mal  stress  exists  to  propagate  it.  This  would  be  the 
case,  for  example,  in  a  tension  test  if  the  pileup 
were  of  sufficient  size  to  generate  a  Griffith  crack. 
The  background  tensile  stress  could  drive  the 
crack  (nucleated  via  shear  stresses)  through  the 
material  to  cause  fracture.  If  the  nucleated  crack  is 
not  favorably  oriented  to  the  backgound  stress  or 
if  the  stress  is  of  insufficient  magnitude,  it  will 
come  to  rest  within  the  material. 

In  compression,  the  nucleated  cracks  generally 
do  not  propagate.  Initially,  the  background  com¬ 
pressive  stress  generates  shear  stresses  along  favor¬ 
ably  oriented  slip  planes,  giving  rise  to  dislocation 
piieups,  as  in  the  tensile  case.  Once  the  crack  is  nu¬ 
cleated,  the  compressive  stress  is  not  capable  of 
propagating  the  crack.  Instead,  the  crack  comes  to 
rest  when  the  strain  energy  associated  with  the 
pileup  is  dissipated  or  when  the  leading  edge  of  the 
crack  reaches  a  barrier  that  it  cannot  overcome, 
such  as  the  change  in  lattice  orientation  occurring 
at  a  grain  boundary. 

Visual  observations  (St.  Lawrence  and  Cole 
1982,  Currier  1983)  reveal  a  strong  tendency  for 
non-propagating  cracks  to  form  roughly  parallel 
to  the  loading  axis  in  uniaxial  compression  tests  on 
randomly  oriented,  equiaxed  polycrystalline  ice. 


s 


Nucleation  conditions  for  more  elaborate  con¬ 
figurations  of  dislocation  sign  and  slip  plane-crack 
geometry  are  also  given.  Again,  as  in  Stroh’s  an- 


Figure  2.  Most  favorable  crack 
orientation  (after  Stroh  1957). 


This  is  reasonable  considering  Stroh’s  determina¬ 
tion  of  the  most  favorable  angle  between  the  slip 
plane  and  the  nucleated  crack.  F  igure  2  shows  the 
geometry  of  this  situation.  The  slip  plane  is  taken 
at  an  angle  of  45°  to  the  loading  axis. 

Although  the  slip  plane  (i.e.  basal  plane)  could 
be  at  an  angle  other  than  the  45"  shown,  the 
planes  of  maximum  resolved  shear  stress  will  tend 
to  cluster  about  this  value.  Also,  Smith  and  Barn- 
by  (1967)  have  shown  that,  while  Stroh’s  optimum 
value  of  =  70.5°  is  correct,  o  may  easily  range 
from  0  to  90°  when  shear  stresses  are  considered  in 
the  analysis.  Even  when  these  values  are  used  as  a 
maximum  range  of  crack  orientation,  the  cracks 
thus  nucleated  will  tend  to  lie  within  about  45 "of 
the  stress  axis  and  have  no  strong  tendency  to 
form  perpendicular  to  it  under  uniaxial  stress. 

Characteristic  size  of  nucleated  crack 

In  examining  fracture  mechanisms  in  metals, 
Gandhi  and  Ashby  (1979)  designated  cracking 
with  no  pre-existing  flaw  as  “cleavage  2.’’  Here 
fractures  are  nucleated  by  slip  or  twinning.  They 
noted  that  these  cracks  were  proportional  to  the 
grain  diameter  and  attributed  this  to  control  by 
the  grain  size  of  the  wavelength  of  the  internal 
stress. 

Physically,  this  proportionality  comes  about  as 
a  result  of  the  obstacle  nature  of  the  grain  boun¬ 
dary.  When  a  polycrystalline  aggregate  is  sub¬ 
jected  to,  say,  a  uniaxial  stress,  the  material  expe¬ 
riences  a  uniform  stress  field  in  a  macroscopic- 
sense.  Microscopically,  however,  this  is  far  from 
the  case:  the  internal  stress  and  strain  fields  are 
very  inhomogeneous. 

Irregularities  in  the  stress  and  strain  fields  are 
brought  about,  in  a  pure  polycrystalline  aggre¬ 
gate,  by  crystal  anisotropy  and  by  dislocation 
movement.  Furthermore,  the  internal  stress  field 
is  in  a  constant  state  of  flux  as  highly  localized  de¬ 
formation  accompanies  both  the  buildup  and  dis¬ 
sipation  of  stress  concentrations  within  the  mate¬ 
rial.  The  frequency  with  which  these  stress  concen¬ 
trations  occur  throughout  the  material  depends 
primarily  on  the  size  of  the  constituent  grains  for 
the  following  reasons. 

The  most  likely  site  for  such  stress  concentra¬ 
tions  is  a  grain  boundary  since  it  offers  a  signifi¬ 
cant  obstacle  to  the  propagation  of  shear  defor¬ 
mation  from  grain  to  grain.  The  most  likely  slip 
plane  is  the  uninterrupted  basal  plane  extending 
across  an  individual  grain.  The  slip  plane  length 
may  or  may  not  equal,  but  in  general  will  scale  as, 
the  grain  size.  Thus,  if  deformation  occurs  via  the 


propagation  of  slip  bands,  the  stress  concentra¬ 
tions  and  their  associated  local  stress  fields  occur 
in  the  material  at  spacings  proportional  to  the 
grain  size.  The  slip  occurs  under  the  action  of 
shear  stress.  However,  the  stress  concentration  re¬ 
sulting  from  slip  generates  a  complex  field  of  ten¬ 
sile,  compressive  and  shear  stresses. 

Gandhi  and  Ashby  (1979)  give  the  expression 
for  a  critical  stress  o*  above  which  a  nucleated 
fracture  will  propagate  and  below  which  the  crack 
will  come  to  rest  with  length  proportional  to  the 
grain  diameter,  d: 

n*  =  (EG./xd)  1  (14) 

where  E  is  Young’s  modulus  and  G,  is  toughness. 

This  is  a  propagation  criterion,  not  a  nucleation 
criterion,  in  that  it  assumes  the  nucleation  of  a 
Griffith  crack  proportional  to  cl.  However,  the  use 
of  a  crack  size  on  the  order  of  d  should  be  noted. 

According  to  Stroh  (1957),  a  nucleated  crack 
will  attain  a  length,  when  normal  background 
stresses  arc  absent,  determined  by  the  number  of 
dislocations  which  enter  it.  Once  the  crack  is  nu¬ 
cleated.  dislocations  enter  it  more  easily  because 
the  back  stress  of  the  pileup  is  relieved.  The  more 
dislocations  that  enter,  the  wider  and  hence  the 
longer  the  crack  becomes.  In  the  compression 
case,  the  only  driving  force  for  the  crack  is  the 
rapidly  relaxing  force  from  the  dislocation  pileup. 
Thus,  the  length  of  the  crack  primarily  is  a  func¬ 
tion  of  the  number  of  dislocations  causing  it  to 
nucleate. 

Generally,  the  analytical  approach  has  been  to 
assume  that  the  favorably  oriented  slip  planes  are 
activated  most  frequently,  and  these  will  in  turn 
nucleate  cracks  most  easily.  If  these  slip  planes 
have  a  characteristic  length,  say  on  the  order  of 
the  grain  diameter,  under  a  given  nominal  stress 
they  will  all  tend  to  contain  about  the  same  num¬ 
ber  of  dislocations.  The  associated  cracks  will  thus 
tend  to  have  a  charcteristic  length  (see  Gold  1966, 
for  example).  Stroh  (1957)  has  indicated  that 
cracks  will  nucleate  and  propagate  to  a  length  on 
the  order  of  f,  the  pileup  length,  in  the  absence  of 
other  driving  stresses. 

However,  the  above  should  be  stated  more  pre¬ 
cisely  in  terms  of  distributions  of  the  quantities 
under  consideration  rather  than  average  or  char¬ 
acteristic  values.  Briefly,  an  estimate  of  the  distri¬ 
bution  of  nucleated  crack  sizes  can  be  obtained  if 
an  appropriate  distribution,  rather  than  an  aver¬ 
age  value,  is  used  to  represent  the  slip  plane 
length.  However,  for  the  purpose  of  demonstra- 


tion  of  the  relationship  between  the  dislocation 
pileup  size  and  the  nucleated  crack  size,  average 
quantities  are  used. 

As  mentioned  above,  grain  boundaries  can  limit 
crack  length.  In  the  case  of  a  uniaxial  compression 
test,  crack  orientation  can  result  in  little  or  no  ten¬ 
sile  stress  normal  to  the  crack  face,  and  a  forming 
crack  may  not  have  a  sufficient  driving  force  to 
overcome  the  crystal  reorientation  at  a  grain 
boundary.  Additionally,  Cottrell  (1958)  viewed 
the  grain  boundary  as  a  likely  stopping  point  for  a 
nucleated  crack  because  a  change  in  orientation  of 
the  cleavage  plane  effectively  represents  a  region 
of  higher  surface  energy  to  the  propagating  micro¬ 
crack.  Thus,  since  grain  boundaries  are  both  likely 
nucleation  and  termination  sites  for  cracks,  the 
crack  size  is  expected  to  correlate  with  the  grain  di¬ 
mension. 

Actual  crack  length  distribution  data  are  un¬ 
common  in  the  literature.  However,  work  by 
McMahon  and  Cohen  (1965)  shows  crack  size  bar 
graphs  for  F4  ferrite  after  repeated  straining  in 
tension.  They  found  that  microcracks  approxi¬ 
mately  equal  to  or  less  than  the  grain  diameter 
formed  first,  and  cracks  up  to  three  times  the 
grain  diameter  formed  after  several  loading  cycles. 
Under  certain  test  conditions,  twin  formation  was 
prevalent  and  the  authors  attributed  a  reduction  in 
the  number  of  large  cracks  to  the  obstacle  nature 
of  the  twins.  Interestingly,  rough  calculations 
based  on  the  bar  graphs  of  McMahon  and  Cohen 
(1965)  indicate  that  the  average  crack  size  is  slight¬ 
ly  over  one  grain  diameter  both  with  and  without 
twin  formation.  They  also  note  that  small  cracks 
continue  to  form  when  the  large  cracks  begin  to 
appear  as  the  number  of  stress  cycles  increases. 

Gold  (1966)  develops  a  quantitative  approach  to 
the  relationship  between  grain  size  and  nucleated 
crack  size  by  using  theory  developed  by  Stroh 
(1954)  and  Bullough  (1964).  Gold  performed  uni¬ 
axial  compression  tests  on  columnar  grained  ice 
and  made  detailed  observations  on  the  size  and 
number  of  microcracks  formed  during  testing. 
Gold's  analysis  considers  the  energy  of  a  cracked 
dislocation  under  an  applied  stress,  and  uses  an 
energy  balance  method  that  leads  to  the  determin¬ 
ation  of  a  critical  or  Griffith  crack.  The  concept  of 
a  cracked  dislocation  as  explained  by  Bullough 
(1964)  allows  the  development  of  a  fracture 
criterion  given  a  dislocation  pileup  and  an  associ¬ 
ated  in-plane  crack  under  an  applied  stress.  The 
fracture  criterion  is  then  based  on  this  crack 
achieving  a  critical  length  for  propagation.  Gold 
(1967)  considers  two  cases  when  the  crack  forms  in 


a  grain  adjacent  to  the  grain  containing  the  pileup: 
1)  the  crack  forms  at  an  angle  to  the  slip  plane 
containing  the  pileup  and  2)  the  crack  forms  in 
plane  with  the  pileup. 

Based  on  the  equations  of  Stroh  (1954)  the 
energy  associated  with  case  1  is 

...  n'b'f t  .  4  L  a„nba 
W  =  T  71  ;  In  —  -  — =- 

4t(1  -  u)  a  2 


al*a\  1  -  v) 
8m 


+  lay 


(15) 


where  W  =  energy  of  the  crack  per  unit  length 
L  =  effective  radius  of  influence  of  the 
dislocations  (L  >  a) 

<r„  =  tensile  stress  perpendicular  to  the 
plane  in  which  the  crack  forms 
a  =  crack  width. 


For  case  2  (Bullough  1964), 


W  = 


n'b'v  4  L 

4*(1  —  v)  n  a 


m'Q-vW. 

8m 


+  lay. 


06) 

Gold  (1966)  derives  critical  values  of  crack  width  a 
for  the  two  cases: 


Case  1 


_  2ny 
*(1  -  v)ai 


(17) 


Case  2 


_  4m7 

*(1  -  u)al 


(18) 


After  assuming  that  a„  is  equal  to  but  of  oppo¬ 
site  sign  than  the  applied  axial  compressive  stress. 
Gold  arrives  at  values  of  a„t,  =  5.7  xlO'4  and  11.4 
x  10'*  m  for  cases  1  and  2,  which  are  in  reasonable 
agreement  with  the  experimental  observations. 
Gold  (1967)  performed  tests  on  replicate  speci¬ 
mens  and  thus  did  not  address  the  issue  of  grain 
size  effects  on  the  cracking  activity  of  the  ice.  In¬ 
deed,  if  the  assumption  regarding  the  value  of  <r. 
being  equal  and  opposite  to  the  applied  stress  is 
maintained,  the  above  expressions  for  critical 
crack  size  are  independent  of  grain  size.  This  is  a 
reasonable  result  when  crack  propagation  is  con¬ 
sidered.  The  cracked  dislocation  is  viewed  as  a  pre¬ 
existing  flaw  and  examined  in  terms  of  its  poten¬ 
tial  to  propagate  under  a  given  stress  field.  The 
potential  (or  likelihood)  for  propagation  is  a  func¬ 
tion  of  material  constants  and  flow  characteris- 


7 


tics,  but  not  specifically  of  grain  size.  Grain  size 
exerts  only  an  indirect  influence  in  that  it  has  an 
effect  on  the  production  of  flaws  in  the  material. 
Thus,  if  consideration  begins  with  the  material  in 
a  flawed  state,  grain  size  is  not  a  primary  consid¬ 
eration. 

The  material  in  the  present  work  is  considered 
to  be  unflawed  and  the  grain  size-dependent  nucie- 
ation  equations  given  earlier  apply.  In  a  subse¬ 
quent  section,  a  simple  method  is  used  to  relate  the 
nucleated  crack  size  to  the  grain  size  through 
strain  energy  and  surface  energy  considerations  in 
a  manner  similar  to  the  above. 

Cracking  in  ice 

A  series  of  papers  by  Gold  (1960;  1965a,b; 
1966;  1967;  1970a,b;  1972;  1977)  represent  the 
most  extensive  investigations  into  the  internal 
cracking  of  ice.  The  experimental  work  primarily 
involves  columnar-grained  ice,  but  many  of  the 
observations  made  are  germane  to  the  behavior  of 
equiaxial-grained  ice. 

In  his  early  work.  Gold  (1960)  noted  the  forma¬ 
tion  of  cracks  parallel  to  the  long  dimension  of 
grains  in  rectangular  ice  specimens.  The  test  mate¬ 
rial  was  grown  to  result  in  random  c-axis  orienta¬ 
tion  in  the  plane  perpendicular  to  the  long  axis  of 
the  grains.  Cracks  formed  parallel  to  the  grain 
boundaries  and  the  planes  of  the  cracks  were  with¬ 
in  45  °  of  the  stress  axis.  A  detailed  analysis  of  a 
number  of  cracks  indicated  that  30%  were  on 
grain  boundaries,  59%  were  transcrystalline  and 
the  remaining  11%  were  of  mixed  character. 

Gold  (1960)  also  noted  a  change  in  the  cracking 
activity  for  stresses  greater  than  approximately  1.5 
MPa  at  a  temperature  of  -10°C.  SpAdmens  were 
tested  under  creep  conditions  and  the  material  was 
columnar-grained  freshwater  ice.  Tne  average 
grain  diameter  perpendicular  to  the  long  axis  of 
the  grains  was  approximately  4  mm.  Below  the 
1.5-MPa  stress,  cracks  were  relatively  sparse  and 
uniformly  distributed;  above  this  stress,  cracking 
activity  increased  significantly  and  the  cracks 
tended  to  cluster  along  planes  of  maximum  shear. 
Cracking  activity  also  tended  to  peak  early  in  the 
tests. 

Continuation  of  work  along  the  same  lines 
(Gold  1967)  demonstrated  that  cracks  generally  in¬ 
volved  only  one  or  two  grains  and  that  they  tended 
to  propagate  either  parallel  or  perpendicular  to  the 
basal  planes.  The  number  of  cracks  that  formed  in 
a  particular  test  depended  mainly  on  stress  and 
creep  strain  levels  and  was  substantially  indepen¬ 
dent  of  temperature.  The  test  material  in  this  work 
was  again  columnar-grained  freshwater  ice  having 


basal  planes  parallel  to  the  long  dimensions  of  the 
grains.  Compressive  loads  were  applied  perpendic¬ 
ular  to  the  long  dimensions  of  the  grains. 

Gold  (1967)  also  suggests  that  the  strength  of  ice 
experiencing  purely  brittle  failure  is  determined  by 
the  level  of  elastic  stresses  that  the  material  can 
sustain.  In  this  case,  rapid  loading  rates  disallow 
significant  plastic  flow.  Plastic  flow  can  occur, 
however,  at  slower  rates  of  loading,  and  internal 
stress  concentrations  capable  of  initiating  cracking 
eventually  develop. 

Gold  (1967)  found  considerable  scatter  in  the 
time  to  first  crack  formation  under  a  given  creep 
stress.  In  general,  the  time  for  a  crack  to  form 
showed  an  exponential  decay  with  increasing  creep 
stress.  Some  straining  occurred  after  load  applica¬ 
tion  during  which  no  cracks  formed.  For  high 
stresses,  some  small  cracks  appeared  upon  and  im¬ 
mediately  following  loading. 

At  a  level  of  creep  strain  between  3  x  10'*  and 
3  x  10'\  large  cracks  (i.e.  greater  than  2  mm  wide 
x  2  mm  long)  began  to  form.  The  rate  of  forma¬ 
tion  built  up  to  a  peak  and  then  gradually  declined 
as  straining  proceeded.  Results  indicated  that  the 
nucleation  of  a  crack  depended  mainly  on  the  level 
of  creep  strain  and  “not  on  factors  controlling  the 
rate  at  which  the  deformation  occurs.”  Gold 
(1967)  also  noted  that  cracks  tended  to  form  in 
grains  having  their  basal  planes  either  perpendic¬ 
ular  or  parallel  to  the  axis  of  applied  stress.  It  was 
in  this  work,  as  mentioned  earlier,  that  Gold  dem¬ 
onstrated  the  applicability  of  a  dislocation  pileup 
mechanism  to  polycrystalline  ice. 

In  subsequent  work,  Gold  (1970a,b)  quantified 
the  cracking  activity  he  observed  in  columnar- 
grained  ice.  He  also  noted,  for  creep  stresses  less 
than  about  1  MPa  at  temperatures  between  -4.8 
and  -31  °C,  that  cracking  was  confined  mainly  to 
primary  creep  and  that  a  clear  secondary  creep 
stage  developed.  For  stresses  over  about  1.2  MPa, 
however,  continuous  cracking  activity  resulted 
and  the  material  passed  directly  from  primary  to 
tertiary  creep  within  2.5  x  I0~’  strain.  He  attrib¬ 
uted  the  onset  of  tertiary  creep  in  his  columnar¬ 
grained  material  to  the  breakdown  of  the  structure 
by  internal  cracking.  However,  it  should  not  be  in¬ 
ferred  from  this  that  cracking  is  necessary  for  ter¬ 
tiary  creep  to  occur  in  ice  in  general.  Mellor  and 
Cole  (1982)  present  test  results  that  show  a  smooth 
transition  from  primary  to  tertiary  creep  in  the 
absence  of  internal  cracking  in  tests  on  equiaxed 
polycrystalline  ice. 

Gold  (1970a,b)  monitored  the  crack  density  by 
counting  the  number  of  cracks  intersecting  a  plane 
perpendicular  to  the  stress  axis.  Values  were  re- 


8 


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I »  .  .  I  *  t  .  1 V  IV  *«. 


ported  in  the  number  of  cracks  per  unit  area.  By 
deforming  specimens  under  various  loads  or  strain 
rates  (as  well  as  at  several  temperatures)  to  given 
levels  of  strain,  Gold  was  able  to  determine  the  in¬ 
crease  in  crack  density  as  straining  proceeded  for  a 
wide  range  of  test  conditions.  These  tests  yielded 
the  following  additional  information.  The  nucle¬ 
ated  cracks  did  not  appear  to  propagate  with  addi¬ 
tional  straining.  The  cracking  rate  depended  on 
stress,  strain  and  temperature.  The  maximum 
cracking  rate  tended  to  occur  between  axial  strains 
of  1 .5  x  10"1  to  2.5  x  10"’.  For  stresses  below  about 
1  MPa,  the  cracking  rate  tended  to  zero  as  strain¬ 
ing  proceeded.  At  greater  stresses,  cracking  con¬ 
tinued  at  a  reduced  rate  after  the  cracking  rate 
maximum  was  reached.  Cracks  were  randomly 
distributed  in  the  ice  at  low  strains  under  all  test 
conditions.  But  at  higher  stresses  they  tended  to 
form  in  bands  or  “fault  planes”  after  the  maxi¬ 
mum  cracking  rate  had  occurred. 

Although  Gold  did  not  observe  fully  brittle  be¬ 
havior  in  these  tests,  he  did  find  a  decrease  in  the 
strain  at  which  the  strain  rate  minimum  occurred 
with  increasing  cracking.  As  cracking  became 
more  severe,  the  strain  associated  with  the  transi¬ 
tion  to  tertiary  creep  decreased  from  levels  over 
101  to  less  than  2.5  xl0‘5.  He  noted,  however, 
that  even  when  the  lowest  strains  were  observed, 
the  material  response  was  still  significantly  ductile 
in  character. 

Additional  work  (Gold  1972)  reinforced  his  ear¬ 
lier  observations  on  cracking  activity.  He  also  de¬ 
veloped  the  stress  dependency  of  cracking  and  in¬ 
vestigated  the  statistics  of  the  cracking  activity.  He 
found  that  the  crack  sites  are  not  truly  random 
throughout  the  specimen,  but  rather  that  the  prob¬ 
ability  of  a  crack  nucleating  in  a  region  decreases 
if  that  region  already  contains  a  crack. 

Using  Weibull  statistics,  Gold  (1972)  inferred 
the  existence  of  two  separate  crack  distributions. 
One,  believed  to  represent  cracks  generated  by  the 
pileup  mechanism,  was  strain  dependent.  The 
other  distribution  represented  cracks  formed  by 
processes  essentially  independent  of  specimen 
strain;  these  cracks  formed  mainly  at  grain  boun¬ 
daries.  The  probability  of  their  occurrence  in¬ 
creased  with  increasing  applied  stress.  Gold  specu¬ 
lates  that,  given  sufficient  stress,  the  type  of 
strain-independent  cracking  could  be  extensive 
enough  to  be  the  sole  cause  of  specimen  failure.  In 
this  work,  Gold  also  noted  that  crack  density  de¬ 
creased  with  temperature  for  a  given  strain  at  con¬ 
stant  stress. 


'VV'  ■"* 

-  r  j  ’  ■  »  V  ’j 


In  a  review  paper.  Gold  (1977)  pointed  out  the 
need  for  an  increased  understanding  of  the  factors 
influencing  the  cracking  activity  in  ice  as  it  relates 
to  the  ductile-to-brittle  transition,  emphasizing  ice 
type,  temperature,  loading  conditions,  grain  size 
and  specimen  size.  Some  Soviet  workers  have  con¬ 
ducted  work  along  a  similar  line  to  that  of  Gold. 
Zaretsky  et  al.  (1976)  presented  the  results  of  a 
study  on  microcrack  formation  in  columnar¬ 
grained  ice.  As  in  Gold’s  work,  load  was  applied 
perpendicular  to  the  long  axes  of  the  grains  and  the 
c-axes  were  randomly  oriented  in  a  plane  perpen¬ 
dicular  to  the  long  axes  of  the  grains.  They  relied 
heavily  on  the  acoustic  emissions  (AE)  monitoring 
technique  to  quantify  the  cracking  activity.  This 
technique  was  first  used  on  ice  by  Gold  (1960), 
who  subsequently  abandoned  it  and  relied  on  vis¬ 
ual  methods  to  estimate  the  number  of  internal 
fractures. 

The  AE  technique  employs  piezoelectric  trans¬ 
ducers  to  monitor  stress  waves  generated  by  the  in¬ 
itiation  of  a  microcrack.  The  intensity  of  the  stress 
wave  is  assumed  proportional  to  the  magnitude  of 
the  event  that  generates  it.  Electronic  devices  an¬ 
alyze  the  transducer  output  and  characterize  the 
signals  in  various  ways,  depending  on  the  level  of 
sophistication  of  the  particular  system.  A  subse¬ 
quent  section  examines  the  AE  method  in  greater 
detail. 

Zaretsky  et  al.  (1976)  assumed  a  one-to-one  cor¬ 
respondence  between  acoustic  pulses  and  crack 
formation.  Furthermore,  the  amplitude  of  the  AE 
pulse  was  taken  as  proportional  to  the  area  of  the 
crack  that  generated  it.  These  assumptions  were 
substantiated  in  subsequent  work  (Zaretsky  et  al. 
1979). 

Experimentally,  the  Soviet  workers  found  much 
the  same  ice  behavior  as  did  Gold.  Zaretsky  et  al. 
(1976)  found  a  threshold  stress  for  crack  nuclea- 
tion  (denoted  as  as),  The  cracks  tended  to  form 
along  the  grain  boundaries  of  the  columnar- 
grained  test  material.  The  ice  deformed  primarily 
in  two  dimensions— as  also  noted  by  Gold.  Com¬ 
plete  breakup  of  the  specimens  occurred  at  some 
appropriate  level  of  crack  density.  The  number 
and  rate  of  formation  of  microcracks  increased 
with  increasing  applied  stress. 

Zaretsky  et  al.  (1976)  developed  an  equation  for 
the  short-term  ice  creep  rate  in  terms  of  the  ac¬ 
cumulated  number  of  defects  (microcracks),  stress 
and  two  parameters.  By  relying  heavily  on  there 
being  a  relatively  constant  number  of  cracks  at  the 
point  of  “breakup,”  they  developed  expressions 
for  the  time  to  break  up  under  a  given  stress. 


v>A-  v\-  • 


a\;  v  ■>*.  y-y-y-y. 
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I 


bo 


By  coupling  ice  straining  solely  with  the  occur¬ 
rence  of  internal  cracking  (as  detected  by  AE),  this 
work  inherently  recognizes  cracking  as  the  only 
deformational  mechanism. 

Zaretsky  et  al.  (1979)  expanded  on  much  of  the 
work  presented  in  Zaretsky  et  al.  (1976).  The 
threshold  stress  am  was  viewed  as  the  stress  above 
which  the  “progressive  accumulation  of  structural 
defects  occurs.”  Since  the  accurate  assessment  of 
the  extent  of  internal  cracking  was  critical  to  the 
evaluation  of  the  analytical  expressions  of  this 
work,  Zaretsky  et  al.  (1979)  presented  the  results 
of  a  detailed  petrographic  analysis  on  tested  speci¬ 
mens.  The  results  showed  structural  changes  (i.e. 
the  breakup  of  large  grains)  as  straining  pro¬ 
ceeded.  This  gave  an  indication  of  the  extent  of  in¬ 
ternal  cracking  since  it  was  crack  formation  that 
broke  up  the  large  original  grains  into  smaller 
grains. 

Zaretsky  et  al.  (1979)  concluded  that  the  thresh¬ 
old  stress  a  ,  in  uniaxial  compression,  is  inde¬ 
pendent  of  temperature.  Furthermore,  from  meas¬ 
urements  of  crack  areas,  it  appeared  that  the  mean 
crack  size  increased  with  the  extent  of  cracking 
(and  thus  with  creep  stress).  Crack  size  was  given 
in  arbitrary  units,  however,  and  thus  a  direct  com¬ 
parison  between  crack  size  and  the  grain  size 
(which  ranged  from  2  to  12  mm)  is  not  possible. 
The  analytical  result  was  an  expression  for  creep 
strain  as  a  function  of  stress,  temperature  and  a 
cracking-related  term  based  on  AE  data. 

Detection  of  internal  fracturing 
by  acoustic  emission  techniques 

Information  provided  by  acoustic  emissions 
(AE)  monitoring  can  contribute  significantly  to 
the  understanding  of  material  behavior.  Micro- 
fracturing  activity  especially  lends  itself  to  inter¬ 
pretation  by  AE  techniques  because  pressure 
waves  generated  during  fracture  formation  are 
easily  detected.  The  main  concern  in  handling  AE 
data  is  that  of  interpretation— determining  the  ap¬ 
propriate  correlation  between  the  characteristics 
of  the  source  event  and  the  recorded  AE  signal.  In 
the  present  case,  the  source  event  is  the  formation 
of  a  microcrack  within  the  ice  and  the  relevant  AE 
characteristic  is  signal  amplitude. 

Evans  (1979)  gave  a  theoretical  treatment  of 
acoustical  pulses  generated  by  microfracture  in 
brittle  solids.  He  showed  that  the  amplitude  of 
such  a  pulse  is  a  function  of  crack  geometry,  ap¬ 
plied  stress,  material  properties,  and  distance 
from  the  source.  The  fracture  event  generates  a 
“ringing”  or  oscillation  in  the  crystal  lattice  that 
decays  in  time  and  has  a  characteristic  frequency 


spectrum.  Frequency  analysis  is  often  used  to  dif¬ 
ferentiate  source  mechanisms  where  more  than 
one  mechanism  is  operating.  In  the  present  case, 
however,  only  the  dislocation  pileup  mechanism  is 
assumed  to  be  operating  and  hence  a  frequency 
analysis  is  not  deemed  critical  to  the  investigation. 
The  work  concentrates  primarily  on  the  analysis 
of  AE  pulse  amplitude. 

When  the  size  of  the  AE  source  (i.e.  microfrac¬ 
ture)  varies,  the  peak  AE  signal  strength  varies  as 
well,  all  other  factors  being  equal.  Such  factors  as 
crack  orientation  and  distance  from  the  sensor  can 
cause  significant  differences  in  the  signal  recorded 
for  otherwise  identical  sources.  Thus  it  should  be 
kept  in  mind  that  the  distributions  generally  given 
for  AE  amplitude  reflect  not  only  variations  in  the 
source  itself  but,  to  some  extent,  second-order 
variables  as  well. 

AE  amplitude  data  are  best  manipulated  in  the 
form  of  distribution  functions.  Pollock  (1981)  de¬ 
scribed  the  most  commonly  used  distributions  and 
discussed  their  pros  and  cons.  Among  those  pre¬ 
sented  were  the  Weibull  and  the  log-normal  distri¬ 
butions  as  well  as  the  extreme  value  distributions. 
That  work  also  traced  the  development  of  several 
models  developed  specifically  for  AE  data  analy¬ 
sis.  He  emphasized  that  the  amplitude  distribution 
can  be  considered  a  property  of  the  source  mecha¬ 
nism.  This  last  point  is  a  common  thread  in  much 
AE  work. 

Ono  et  al.  (1978)  showed  close  correlation  be¬ 
tween  the  particle  size  distribution  of  Mn-S  inclu¬ 
sions  in  steel  and  the  AE  amplitude  distribution 
found  when  the  particles  fractured  during  testing. 
Thus,  the  particle  size  governed  the  crack  size, 
which  in  turn  governed  the  amplitude  distribution. 
Wadley  et  al.  (1981)  and  Cousland  and  Scala 
(1981)  are  other  examples  of  work  directed  at  link¬ 
ing  acoustic  activity  and  specific  microstructural 
characteristics. 

In  certain  cases,  AE  also  proves  useful  in  eli¬ 
minating  certain  deformational  mechanisms  from 
consideration.  For  example,  in  Cousland  and 
Scala  (1981),  inclusion  fracture  was  observed  in 
tension  testing  and  produced  very  high  amplitude 
emissions.  When  the  same  material  was  tested  in 
compression,  inclusion  fracture  did  not  occur  and 
no  high  amplitude  AE  signals  were  observed,  thus 
giving  a  clear  indication  of  the  source  mechanism 
in  the  tensile  case.  With  such  information  on  the 
material,  the  extent  of  inclusion  fracture  could  be 
reliably  determined  under  other  test  conditions 
without  extensive  metallographic  investigation. 
Note,  however,  that  quantitative  applications  of 


t1.  -" ,  A.  A  A  A  4 St (  *  A-V*  “  o.  • 


-.  ■.  \ 


10 


i  --■  1 


AE  require  a  correlation  between  specific  charac¬ 
teristics  of  both  the  deformational  process  and  the 
recorded  AE  signals. 

Wadley  et  al.  (1981)  indicated  the  capability  of 
AE  analysis  to  discriminate  between  two  possible 
event  sources  on  the  basis  of  differences  in  the  AE 
signatures.  By  examination  of  cleavage  and  inter¬ 
granular  crack  sizes  they  noted  that  intergranular 
cracks  were  significantly  larger  on  average  and 
they  corresponded  well  with  the  observed  number 
of  high  amplitude  emissions.  The  particular  equip¬ 
ment  settings  used,  however,  prevented  proper  ac¬ 
quisition  of  the  low  amplitude  signals  resulting 
from  the  smaller  cleavage  fractures. 

Several  studies  have  explored  the  grain  size  ef¬ 
fect  on  internal  fracturing  using  AE  techniques. 
Khan  et  al.  (1982)  found  AE  activity  to  increase 
with  grain  size  for  several  types  of  steel.  Scruby  et 
al.  (1981)  found  similar  trends  for  aluminum  and 
an  aluminum-magnesium  alloy. 

The  optical  clarity  of  ice  and  its  propensity  for 
microfracture  under  conditions  of  practical  inter¬ 
est  make  it  ideally  suited  to  study  with  AE  tech¬ 
niques.  Gold  (1960)  recognized  this  fact  and  was 
the  first  to  use  a  piezoelectric  transducer  to  moni¬ 
tor  cracks  in  ice.  Interpretational  difficulties, 
however,  led  him  to  estimate  internal  cracking  by 
direct  visual  means  in  subsequent  work.  The  po¬ 
tential  benefit  of  the  AE  method  was  clear,  but  the 
equipment  of  the  day  did  not  prove  adequate. 

Work  by  Zaretsky  et  al.  (1979),  mentioned  ear¬ 
lier  in  another  connection,  used  AE  data  directly 
in  a  constitutive  relationship  for  ice.  This  was  pos¬ 
sible  because,  for  certain  test  conditions,  the  ac¬ 
cumulated  acoustic  pulses  followed  the  form  of 
the  accumulated  creep  strain.  This  1979  paper  re¬ 
fers  to  Zaretsky  et  al.  (1976)  for  the  development 
of  a  functional  relationship  between  the  AE  sig¬ 
nals  and  the  corresponding  formation  of  micro- 
cracks.  The  expression  for  creep  strain  was  formu¬ 
lated  as  the  product  of  the  number  of  acoustic 
pulses,  the  mean  crack  size  and  a  proportionality 
factor.  The  mean  crack  size  was  determined 
through  an  analysis  of  the  acoustic  event  ampli¬ 
tudes  by  assuming  that  AE  amplitude  is  a  function 
of  microcrack  size. 

Zaretsky  et  al.  (1979)  also  show  a  close  correla¬ 
tion  between  the  microcrack  surface  area  and  the 
number  of  accumulated  defects.  The  expected  sur¬ 
face  area  increased  linearly  with  the  number  of 
acoustic  pulses  recorded.  The  final  expression 
given  for  ice  creep  in  this  work  showed  time- 
dependent  strain  as  a  function  of  defect  accumula¬ 
tion  measured  by  AE,  temperature,  stress  and 
time. 


II 


The  success  of  this  approach  relies  heavily  on 
the  ability  to  determine  precisely  the  number  of 
cracks  occurring  in  time  from  the  AE  data.  This  is 
a  difficult  task  given  the  variability  of  AE  moni¬ 
toring  systems.  Additionally,  this  approach  is 
valid  only  when  processes  other  than  crack  forma¬ 
tion  do  not  significantly  contribute  to  straining. 

More  recently,  St.  Lawrence  and  Cole  (1982) 
and  Cole  and  St.  Lawrence  (1984)  applied  AE 
techniques  to  monitor  microfracturing  in  poly¬ 
crystalline  ice  having  equiaxed  grains  (in  contrast 
to  the  columnar-grained  material  tested  in  the 
abovementioned  works),  initial  grain  size  was  held 
constant  in  these  experiments  at  1.2  mm  as  deter¬ 
mined  by  the  intercept  method.  Equipment  limita¬ 
tions  prevented  a  direct  correlation  between  AE 
amplitude  and  crack  size.  Instead,  AE  activity  re¬ 
corded  at  two  sensitivity  levels  was  only  assumed 
to  parallel  the  actual  cracking  activity.  The  expres¬ 
sion  developed  for  acoustic  activity  showed  a  de¬ 
pendency  on  stress  and  time.  In  the  creep  tests  re¬ 
ported  in  the  former  paper,  the  AE  rate  reached  a 
maximum  at  1.8x10'’  axial  strain  and  then 
dropped  sharply  as  deformation  proceeded.  For 
stresses  of  less  than  about  2.35  MPa,  the  AE  rate 
after  the  initial  4  x  10  ’  strain  was  extremely  low. 
Stresses  over  3.26  MPa,  on  the  other  hand,  in¬ 
duced  considerable  AE  activity  after  the  rate  peak, 
indicating  a  significant  amount  of  additional  mi¬ 
crofracture. 

In  this  study,  the  acoustic  activity  ranged  over 
some  three  orders  of  magnitude  as  stress  increased 
from  0.8  to  3.67  MPa.  Interestingly,  although  the 
test  material  reached  virtually  complete  saturation 
with  internal  cracks,  the  overall  behavior  could  be 
reasonably  described  as  ductile  since  typical  creep 
behavior  was  still  evidenced  and  the  strain  at  the 
creep  rate  minimum  did  not  decrease. 

In  the  constant  rate  of  deformation  tests  report¬ 
ed  in  Cole  and  St.  Lawrence  (1984),  the  highest 
strain  rates  did  bring  about  substantially  brittle 
behavior.  For  stresses  in  excess  of  5  MPa  and 
strain  rates  over  10“  s  ',  characteristic  failure 
strains  dropped  to  values  as  low  as  2.3  x  10  ’. 
Ductile-type  failures  occur  near  10'!  axial  strain. 
Strain  rates  near  10“  s'1  at  -5°C  resulted  in  virtu¬ 
ally  no  visible  cracking.  An  increase  to  roughly 
10“  s  '  results  in  a  significant  loss  in  ductility  as 
indicated  by  the  occurrence  of  both  a  high  degree 
of  internal  fracture  and  a  reduction  in  the  axial 
strain  associated  with  the  peak  stress. 

In  both  the  creep  and  strength  tests  reported, 
the  onset  of  cracking  as  indicated  by  the  AE  activi¬ 
ty  occurred  at  approximately  10"’  axial  strain. 


f 


•V* 

•Vo 


$ 


ri'A 


••>1 


.  f. 


Stress  at  the  onset  of  visible  cracking  was  generally 
near  2.0  MPa  at  -5°C. 

In  other  recent  work,  Sinha  (1982)  monitored 
the  acoustic  activity  in  columnar-grained  ice  in 
uniaxial  compressive  strength  tests.  He  noted  fair¬ 
ly  uniformly  distributed  cracks  that  were  compar¬ 
able  in  size  to  the  grains.  Visible  cracking  gener¬ 
ally  began  at  2.4  x  10'4  strain  and  at  stress  near  0.8 
MPa. 

Sinha  (1982)  associated  visible  cracking  with 
acoustic  event  amplitudes  of  79  dB  with  his  partic¬ 
ular  system.  He  used  visual  observation  during 
testing  to  help  establish  this  cutoff  level. 

As  in  St .  Lawrence  and  Cole  ( 1 982),  Sinha  ( 1 982) 
found  some  low  level  AE  activity  at  the  small 
strains  prior  to  the  onset  of  visible  cracking. 


TEST  METHODS 

This  section  describes  the  testing  methods  and 
procedures  employed  in  the  laboratory  work.  The 
specimen  preparation  procedure  and  the  creep 
testing  equipment  have  been  described  in  detail 
elsewhere  (Cole  1979,  Mellor  and  Cole  1982)  and 
are  covered  only  briefly  here.  However,  the  meth¬ 
od  of  grain  size  analysis  and  the  post-test  analysis 
of  internal  cracking  receive  close  scrutiny. 

Specimen  preparation 

The  specimen  preparation  method  developed  by 
Cole  (1979)  produces  polycrystalline  ice  with  ran¬ 
domly  oriented,  equiaxed  grains  and  densities  of 
0.917  ±0.003  Mg/mJ.  Grain  size  can  vary  up  to 
the  practical  limit  established  by  the  mold  size  and 
is  controlled  by  the  grain  size  of  the  seed  crystals. 
The  specimens  are  50.8  mm  in  diameter  and  127 
mm  long. 

The  method  calls  for  filling  a  cylindrical  alumi¬ 
num  mold  with  the  appropriate  size  seed  grains, 
sealing  the  mold  and  applying  a  vacuum  of  13-26 
Pa  for  2.5  hr.  Distilled,  degassed  water  at  0°C  then 
fills  the  mold  under  the  action  of  the  vacuum. 
Once  this  flooding  is  complete,  the  mold  is  placed 
in  a  freezing  coil  which  carries  fluid  from  a 
temperature  bath  at  -5°C.  The  degassed  water  is 
flushed  up  through  the  mold  as  the  radial  freezing 
progresses  at  an  average  rate  of  2.8  /rni/s.  The 
continuous  flushing  helps  prevent  bubble  nuclea- 
tion  and/or  growth  by  keeping  the  dissolved  gas 
concentration  low  in  the  pore  water. 

The  freezing  process  often  results  in  a  thin  col¬ 
umn  of  fine  bubbles  along  the  axis  of  the  speci¬ 
men.  This  occurs  when  the  freezing  process  pre¬ 
maturely  closes  off  the  path  of  the  flushing  water 


Figure  3.  Typical  untested  specimen. 


near  one  end  of  the  specimen.  The  bubbles  form 
when  the  remaining  gas-laden  pore  water  freezes. 

Figure  3  shows  a  typical  fine-grained  specimen 
produced  by  this  method.  The  end  caps  are  fixed 
in  the  mold  to  assure  proper  alignment.  They  are 
made  from  a  fabric-based  phenolic  material.  The 
ice  bonds  well  to  this  material  once  the  factory  fin¬ 
ish  has  been  roughened  to  expose  the  fabric. 

Specimens  emerged  from  this  procedure  near  a 
temperature  of  -5°C  and  were  placed  in  the  creep 
apparatus  at  -5°C  if  they  were  to  be  tested  imme¬ 
diately.  If  short-term  storage  was  required,  they 
were  wrapped  in  several  layers  of  polyethylene 
film  and  placed  in  ice-filled  bags  and  kept  at 
-12°C.  Such  specimens  equilibrated  at  the  -5°C 
test  temperature  for  at  least  24  hr  prior  to  testing. 

Creep  testing  apparatus 

The  creep  apparatus  and  environmental  control 
cabinet  are  described  in  Mellor  and  Cole  (1982). 
The  end  caps  bolt  into  the  base  and  loading  piston 
of  the  test  fixture.  A  pneumatically  actuated  cylin¬ 
der  applies  the  desired  load  to  the  specimen 


12 


Figure  4.  Creep  testing  apparatus  showing  dis¬ 
placement  transducer  and  mounting  clamps  on 
specimen. 

through  a  50.8-mm-diameter  steel  piston.  The  pis¬ 
ton  is  mounted  in  a  large  linear  ball  bushing  to  en¬ 
sure  virtually  friction-free  movement. 

The  calibration  procedure  associated  the  output 
of  a  transducer,  which  monitored  the  supply  pres¬ 
sure  to  the  actuator,  to  the  load  exerted  by  the  pis¬ 
ton  on  a  standard  load  cell.  This  method  account¬ 
ed  for  all  frictional  losses  in  the  system. 

The  test  fixture  maintained  the  end  caps  parallel 
during  deformation.  Therefore,  only  one  trans¬ 
ducer  was  required  to  monitor  the  axial  deforma¬ 
tion.  A  direct  current  displacement  transducer 
(DCDT)  with  a  linear  range  of  ±3.175  mm  was 
employed.  Two  circumferential  clamps  held  the 
DCDT  core  and  barrel.  Figure  4  shows  the  com¬ 
plete  creep  testing  apparatus  along  with  the  DCDT 
and  mounting  configuration. 

An  analog  to  digital  data  logger  recorded  the 
DCDT  output  along  with  the  output  of  the  pres¬ 
sure  transducer  and  the  time  of  each  reading.  The 
sampling  time  of  the  data  logger  ranged  from  15  s 


at  the  start  of  a  test  to  as  high  as  300  s  at  higher 
strains  and  slow  strain  rates.  A  separate  system 
continuously  monitored  the  test  temperature, 
which  varied  less  than  ±0.1°C  during  testing. 

Crack  length  and  crack  density  measurements 

After  testing,  specimens  were  moved  to  a  -10°C 
work  room  for  sectioning  and  photographing. 
Specimens  were  generally  cut  on  a  band  saw  to 
generate  horizontal  and  vertical  sections  (see  Fig. 
5).  These  thick  sections  were  approximately  10 
mm  thick,  but  thickness  varied  depending  upon 
crack  density.  High  crack  density  required  thinner 
sections  in  order  to  distinguish  individual  cracks. 
Thicker  sections  could  be  used  when  the  crack 
density  was  low. 

The  horizontal  sections,  taken  perpendicular  to 
the  stress  axis,  were  used  to  estimate  crack  densi¬ 
ties  and  to  measure  crack  lengths.  Since  the  cracks 
tended  to  form  parallel  to  the  stress  axis,  the  hori¬ 
zontally  oriented  sections  showed  the  cracks  in  an 
edge-on  view.  From  this  vantage  point,  the  cracks 
generally  appeared  as  well-defined  lines  and  were 
easily  measured.  The  vertically  oriented  sections, 
while  allowing  measurement  of  crack  dimensions 
parallel  to  the  stress  axis  to  a  certain  extent,  did 
not  provide  an  accurate  means  of  counting  and 
measuring  every  crack  in  the  section.  Inaccuracies 
arose  in  this  case  because  some  cracks  were  seen 
face-on  and  tended  to  obscure  the  view  of  cracks 
which  were  located  behind  them  in  the  section. 


Figure  5.  Schematic 
showing  typical  locations 
of  thick  sections  in  the 
cylindrical  ice  specimens. 
Numbers  1-3  are  horizontal 
sections  used  for  crack  den¬ 
sity  measurements. 


The  question  naturally  arises  as  to  whether  the 
measurement  of  crack  length  in  the  horizontal  sec¬ 
tions  is  an  accurate  representation  of  the  true 
crack  length.  Also,  the  validity  of  the  use  of  one 
length  measurement  to  represent  the  size  of  a 
crack  must  be  established.  These  points  will  be  dis¬ 
cussed  in  detail  and  data  will  be  presented  to  show 
the  extent  of  the  error  introduced  by  these  as¬ 
sumptions. 

For  most  specimens,  photographs  of  back-light¬ 
ed  thick  sections  were  taken.  From  these  it  was 
possible  to  count  and  measure  all  visible  cracks  in 
the  section.  The  sections  were  divided  into  roughly 
200-mmJ  sectors  and  each  sector  was  photo¬ 
graphed  with  a  7  x  magnifying  camera.  It  was 
then  possible  to  form  a  mosaic  of  the  section,  and 
from  this  the  number  and  lengths  of  cracks  were 
taken. 

In  some  cases,  when  the  crack  density  was  ex¬ 
tremely  low,  it  was  possible  to  make  direct  meas¬ 
urement  from  the  viewer  of  the  camera,  preclud¬ 
ing  the  need  of  taking  photographs.  Also  in  these 
cases,  a  larger  volume  of  material  was  sampled  be¬ 
cause  it  was  considerably  less  time  consuming  to 
make  the  measurements.  The  volume  of  the  sec¬ 
tion  was  recorded,  and  once  the  cracks  were 
counted,  the  number  of  cracks  per  unit  volume 
was  calculated. 


Crack  healing  measurements 

k  The  thick-sectioning  technique  described  in  the 

J  previous  section  provided  a  means  to  monitor  the 

!  change  in  crack  length  with  time.  After  photo- 

‘  graphing  immediately  after  testing,  two  typical 

thick  sections  were  tightly  wrapped  and  placed  in  a 
|  -5°C  environment,  and  they  were  photographed 

■  several  times  during  a  period  of  nearly  eight 

i.  weeks.  This  was  sufficient  time  to  allow  complete- 

J  ly  isolated  cracks  to  transform  from  their  initial 

■  “penny”  shape  to  oblate  spheroids.  The  lengths 
of  the  cracks  were  taken  from  each  photograph, 
and  special  attention  was  paid  to  the  first  hours  of 
the  healing  process.  The  results  help  to  assess  the 
possible  change  in  crack  length  resulting  from  the 

•  healing  process  that  occurred  between  the  time  of 
the  crack’s  formation  and  the  time  the  length 
measurement  was  made. 

k 

£  Thin  section  photographs 

■,  Photographs  were  taken  of  thin  sections  and 

•  provided  the  means  of  determining  grain  size  and 
of  discovering  any  anomalies  in  the  test  material 
(see  Fig.  6).  Photographs  were  taken  of  both  verti¬ 
cal  and  horizontal  sections  in  some  cases,  al- 

■  though  generally  only  horizontal  sections  were 


taken.  Figure  6  shows  thin-section  photographs 
for  several  specimens  of  various  grain  sizes. 

The  thick  sections  used  for  the  crack  density  an¬ 
alysis  were  trimmed  to  a  suitable  thickness  for  the 
thin-section  photograph  immediately  after  the 
crack  density  measurements  were  taken.  The 
amount  of  time  between  testing  and  the  final  thin 
section  photograph  was  usually  on  the  order  of  2 
to  4  hours.  Significant  grain  growth  was  not  as¬ 
sumed  to  occur  within  this  time. 

Grain  size  determination 

There  are  several  methods  that  can  be  used  to 
estimate  polycrystalline  grain  size.  A  summary  of 
various  methods  is  given  by  Dieter  (1976)  and  they 
are  briefly  described  below. 

Mean  intercept  length 

Grain  diameter  is  found  by  dividing  the  total 
length  of  a  test  line  by  the  number  of  grains  inter¬ 
sected  when  the  line  is  placed  randomly  on  the  sec¬ 
tion.  This  generally  underestimates  the  true  diam¬ 
eter  of  equiaxed  grains,  but  is  accurate  for  colum¬ 
nar  grains  viewed  perpendicular  to  the  long  axes. 

Grains  per  unit  area 

Assuming  constant  size  spherical  grains,  the 
grain  size  may  be  estimated  by 


where  M  is  the  number  of  grains  per  unit  area. 

A  STM  standard  charts 

Grain  size  at  a  fixed  magnification  is  compared 
with  standard  ASTM  grain  size  charts  and  a  grain 
size  number  is  established.  This  method  will  not  be 
considered  in  the  present  work. 

The  apparent  grain  size  in  the  plane  of  the  sec¬ 
tion  can  also  be  estimated  from  measurements  of 
grains  per  unit  area  M.  In  this  case,  we  find  the 
diameter  which  corresponds  to  the  average  area 
per  grain  1/M,. 


Average  area  = 


t  D‘ 
4 


l  =  lEL 

M  4 


(20) 


14 


This  results  in  a  somewhat  smaller  estimate  of 
grain  size  than  eq  19.  The  test  results  section  gives 
a  comparison  of  the  grain  sizes  obtained  using 
each  of  the  above  methods.  There  are  significant 
differences  in  grain  size  estimates  depending  on 
the  method  used.  Since  the  work  at  hand  requires 
estimates  of  the  true  grain  size,  and  not  merely 
values  that  scale  as  the  grain  size  (such  as  the  re¬ 
sults  of  the  intercept  method),  the  estimates  result¬ 
ing  from  eq  19,  which  give  the  largest  values,  will 
be  used  in  all  analyses.  The  chosen  method  relies 
on  the  assumption  that  the  grains  are  of  uniform 
size  and  spherical  shape.  Neither  of  these  is  true; 
however,  they  appear  useful  because  the  seed 
grains  are  sieved  to  within  ±8°7o  of  the  average 
seed  size  and  the  seed  grains  are  roughly  equiaxed. 

Caution  must  be  exercised  in  comparing  this 
work  with  other  analyses  in  which  grain  sizes  were 
estimated  with  the  intercept  technique.  As  noted, 
the  grain  sizes  calculated  using  eq  19  are  larger 
than  those  found  with  the  intercept  method  for  the 


present  data.  This  increase  is  significant  and 
should  be  taken  into  account  wherever  grain  size 
measurements  are  of  critical  importance.  In  a  re¬ 
lated  area,  it  should  be  mentioned  that  the  method 
used  to  determine  grain  size  will  influence  the 
slope  of  a  Hall-Petch  type  plot. 

Acquisition  of  acoustic  emission  data 

A  microcomputer-based  AE  system  monitored 
the  acoustic  activity  in  all  tests.  The  system  em¬ 
ployed  two  piezoelectric  transducers  mounted  as 
seen  in  Figure  7.  Elastic  bands  attached  to  the 
mounting  shell  hold  the  transducers  in  place.  Ice 
fillets  formed  from  distilled  water  served  to  in¬ 
crease  the  contact  area  between  the  side  of  the 
specimen  and  the  flat  transducer  face.  A  thin  layer 
of  silicone  grease  between  the  transducer  and  the 
ice  assured  good  acoustic  coupling. 

The  AE  system,  a  PA C  3400  by  Physical  Acous¬ 
tics  Corporation,  recorded  characteristics  of  the 
AE  pulses,  but  not  the  actual  pulse  itself.  Figure  8 


Figure  7.  AE  transducer  mounted  on  specimen.  Trans¬ 
ducers  are  placed  on  flat  contact  points. 


XOCR  Output 


Peok 

Amplitude 

— - Threshold 

- — * 

Timt 


Figure  8.  Idealized  acoustic  emission  waveforms. 


shows  an  idealized  AE  waveform  and  identifies 
the  major  characteristics  recorded  by  the  system. 
The  gain,  or  amplification  level,  and  the  thresh¬ 
old,  or  cut-off  voltage,  together  determine  the 
overall  sensitivity  of  the  system.  For  these  tests, 
the  gain  was  set  at  60  dB,  which  corresponds  to  an 
amplification  of  1000  times  the  signal  sensed  by 
the  transducer.  The  threshold  setting  varied  some¬ 
what  depending  on  the  AE  activity  level.  St.  Law¬ 
rence  and  Cole  (1982)  point  out  that,  in  ice,  both 
visible  cracking  ana  aetormational  processes 
which  result  in  no  visible  discontinuities  generate 


detectable  acoustic  activity.  Higher  amplitude 
events,  however,  are  expected  from  the  visible 
cracks  as  a  result  of  the  greater  strain  energy  asso¬ 
ciated  with  crack  nucleation.  The  settings  used  in 
this  work  were  such  that  the  AE  system  responded 
to  event  amplitudes  somewhat  below  that  resulting 
from  visible  cracks,  thus  assuring  that  all  the  visi¬ 
ble  cracking  events  were  recorded. 

The  AE  amplifier  band-pass  filters  the  signal  in 
the  range  10  to  200  kHz.  Earlier  work  (St.  Law¬ 
rence  and  Cole  1982)  showed  this  range  to  be  suit¬ 
able  for  monitoring  cracks  in  ice. 


Table  1.  Creep  data. 


Specimen 


'max 
(X  I0'J 


1.5 

2.0 

5.0 

1.8 

2.0 

5.0 

1.8 

2.0 

1.0 

1.8) 

2.0 

0.2 

2.6 

2.0 

5.0 

2.8 

2.4 

1.0 

2.9 

2.0 

4.8 

3.2 

2.8 

1.0 

3.2 

2.0 

1.0 

«  Ot  >mm 
(x  to  V 


' min 

s"  (xl0  ‘ ) 


Time  to  min 
(s) 


*  °t  >  mm 
(x  !0  'i 


•  Grain  size  achieved  by  grain  growth  process. 

NOTE:  Specimens  that  have  no  values  given  for  and  c  at  toy,  were  not  strained  sufficiently  to  ex¬ 
perience  a  strain  rate  minimum. 


PRESENTATION  OF  RESULTS 


Specimen  characteristics 

Table  1  gives  a  list  of  the  specimens  tested,  the 
initial  applied  stress  level,  the  maximum  axial 
strain  before  removal  of  the  load,  and  the  axial 
strain  at  which  the  minimum  strain  rate  occurred. 

Table  2a  shows  the  specimen  grain  sizes  as  de¬ 
termined  by  the  intercept  method  and  two  meth¬ 
ods  based  on  measurements  of  grains  per  unit 
area.  As  noted  earlier,  the  results  given  in  the  third 
column,  found  using  eq  19,  are  used  in  all  subse¬ 
quent  work  to  characterize  the  material.  These 
values  tend  to  be  significantly  larger  (52.5%  on 
average)  than  those  found  with  the  often  used  in¬ 
tercept  method. 

Table  2b  gives  a  comparison  of  the  three  meth¬ 
ods  of  grain  size  estimation  based  on  thin  sections 
of  untested  material.  The  seed  size  refers  to  the 
sieve  size  range  of  the  ice  crystals  used  to  form  the 
specimen.  Note  that  the  intercept  method  yields 
grain  size  estimates  that  are  smaller  than  the  ori¬ 
ginal  seed  grains.  As  discussed  earlier,  the  method 
used  in  this  work  ( d ,)  gives  estimates  that  are 
slightly  larger  than  the  seed  grains,  but  these  esti¬ 
mates  are  reasonable  because  the  average  seed 
grain  diameter  is  expected  to  increase  as  the  grain 
grows  into  the  adjacent  pore  space  during  freez¬ 
ing. 

Microcrack  measurements 

As  described  above,  post-test  observations  yield 
the  number  and  size  of  cracks  in  a  given  volume  of 
material.  When  the  crack  density  was  very  low,  a 
large  volume  of  material  was  sampled,  and  cracks 
were  measured  and  counted  directly  from  the  thin 
section.  Up  to  three  thick  sections  were  evaluated 
from  each  specimen.  These  data  made  it  possible 
to  estimate  the  crack  density  of  the  entire  speci¬ 
men. 

Since  moderate  to  extensive  cracking  levels  re¬ 
quired  photographs  for  accurate  interpretation, 
two  or  three  sections  of  each  specimen  were  pho¬ 
tographed  as  described  earlier.  Generally,  half  a 
longitudinal  thick  section  was  photographed.  As¬ 
suming  radial  symmetry  in  the  crack  distribution, 
these  results  were  used  to  estimate  the  crack  den¬ 
sity  in  the  central  region  of  the  specimen.  The  esti¬ 
mates  of  crack  density  did  not  include  the  ice  near 
the  ends  of  the  specimen  because  the  triaxial  stress 
state  induced  by  the  end  caps  generally  resulted  in 
a  lower  crack  density  in  these  regions.  Thus,  the 
crack  densities  reported  are  assumed  to  be  repre¬ 
sentative  of  the  material  under  a  uniaxial  stress 
state. 


Table  2.  Grain  size  estimates 
and  seed  grain  sizes. 


a.  Grain  size  estimates  lor 
tested  specimens.* 


Sample 

d, 

(mm) 

d, 

(mm) 

d, 

(mm) 

43 

1.3 

1.5 

1.8 

44 

2.3 

2.5 

3.3 

47 

1.7 

2.1 

2.6 

49 

2.4 

2.8 

3.5 

55 

— 

— 

(1.8) 

56 

2.4 

3.4 

4.2 

57 

3.6 

3.9 

4.8 

58 

4.7 

4.2 

5.2 

59 

4.2 

4.2 

5.5 

60 

1.7 

2.4 

2.9 

61 

1.9 

2.8 

3.4 

62 

3.6 

4.6 

4.7 

63 

2.0 

2.6 

3.2 

64 

2.0 

2.7 

3.3 

65 

1.7 

2.3 

2.8 

69 

1.2 

1.3 

1.5 

70 

1.1 

1.5 

1.8 

71 

3.6 

4.5 

5.5 

72 

3.4 

4.2 

4.8 

73 

4.4 

4.4 

5.4 

74 

1.9 

2.6 

3.2 

75 

2.0 

2.6 

3.2 

76 

2.1 

2.8 

3.5 

77 

2.1 

2.6 

3.2 

78 

2.4 

2.8 

3.5 

79 

3.7 

4.8 

6.0 

b.  Seed  grain  sizes  and  resulting  grain 
size  measurements  on  untested  ice. 


Seed 

grain  size 

d, 

d, 

d, 

(mm) 

(mm) 

(mm) 

(mm) 

2.80-3.35 

2.5 

3.1 

3.8 

4.0-4.76 

3.6 

4.1 

5.0 

•  dr.  intercept  method. 
d average  area  method. 
d,:  uniform  sphere  assumption  (eq  19). 


'-'V'v'v'.''.' 


18 


Microfractures 


0  2  4  6  8 

Microfracture  Length  (mm) 

Figure  9.  Typical  crack  length  histogram. 


Table  3.  Crack  location. 


Specimen 

d 

(mm) 

%  GB 
cracks 

V,  XT 
cracks 

49 

3.5 

58 

42 

56 

4.2 

41 

59 

65 

2.8 

SI 

43 

71 

5.5 

54 

46 

72 

4.8 

60 

40 

73 

5.4 

47 

53 

Average 

53  ±7 

47  ±7 

Crack  lengths 

Crack  length  measurements  were  a  direct  result 
of  the  post  test  analysis.  Figure  9  shows  a  typical 
crack  length  histogram.  Appendix  A  contains  all 
the  crack  length  data  presented  in  the  form  of  his¬ 
tograms.  The  average  grain  diameter  is  indicated 
for  each  specimen.  In  some  cases  where  a  more 
detailed  examination  of  the  cracking  was  carried 
out,  transgranular  and  grain  boundary  crack 
histograms  are  shown  separately.  Table  3  gives  the 
mean  values  of  grain  boundary  and  transcrystal- 
line  crack  lengths  obtained  from  these  observa¬ 
tions. 

Figure  10  shows  the  average  crack  length  plot¬ 
ted  against  the  grain  diameter  for  all  cracks,  re¬ 
gardless  of  location.  This  Figure  also  shows  plots 
of  the  least-squares  best-fit  curve  for  all  the  points 
shown  along  with  the  theoretical  curve  to  be  dis¬ 
cussed  later.  The  bars  associated  with  each  point 
indicate  a  bandwidth  of  ±  one  standard  devia¬ 
tion. 

Crack  density 

Figure  11  shows  typical  mosaics  of  the  thick- 
section  photographs.  Each  was  formed  from  five 
enlarged  photographs.  Thin  sections  were  general¬ 
ly  used  to  quantify  the  cracking  activity  for  severe¬ 
ly  cracked  specimens  (Fig.  1  la),  since  the  extensive 
network  of  overlapping  cracks  made  interpreta¬ 
tion  of  the  thick  section  photographs  difficult. 


P'X, 


65 

75  X 

47 

r  z' 

; 

77 

£  , 

43X^ 

631  ' 

2  3  4  5 

Mean  Grain  Diameter  (mm) 


Figure  10.  Mean  crack  length  vs  mean  grain  diameter. 


a.  A  highly  cracked  specimen. 


b.  A  moderately  cracked  specimen. 

Figure  II.  Mosaics  formed  from  enlarged  thick  section  photographs.  Cracks 
show  as  black  lines  of  varying  thickness  under  back  lighting. 


The  crack  density  data,  expressed  as  cracks  per  grain.  Note  that  at  a  constant  initial  stress  of  2.0 

unit  volume,  given  in  Table  4  represent  averages  MPa  crack  densities  range  from  zero  to  nearly  one 

of  several  thick  section  observations  in  most  cases.  crack  per  grain  as  grain  size  increases  from  1.5  to 

Table  4  also  gives  crack  densities  in  terms  of  5.7  mm. 

cracks  per  grain.  These  values  come  about  by  di-  Crack  density  also  increases  with  specimen  strain 

viding  the  observed  number  of  cracks  by  the  esti-  for  all  but  the  smallest  grain  sizes.  Figure  13  shows 

mated  number  of  grains  in  the  sections  under  con-  this  dependency  for  several  grain  sizes, 

sideration.  The  calculation  of  the  number  of  In  some  instances  cracking  in  the  large-grained 

grains  is  based  upon  the  grain  sizes  given  in  col-  specimens  was  so  extensive  that  interpretation  us- 

umn  3  of  Table  2a.  Figure  !2a  gives  plots  of  crack  ing  thick  section  photographs  was  very  difficult, 

density,  in  terms  of  cracks  per  unit  volume,  versus  In  these  cases,  thin  sections  were  prepared  and  the 

grain  size  for  several  ax  tl  strain  levels.  Figure  12b  number  of  cracks  per  grain  was  measured  directly, 

gives  the  same  data  plotted  in  terms  of  cracks  per  The  validity  of  this  procedure  was  checked  by 


Table  4.  Results  of  mtcrofracture  observations. 


Mean  Standard 


d  crack  size  deviation  Mean  _ Crack  density 


Specimen 

(mm) 

(mm) 

(mm) 

d 

(cracks/m') 

(cracks/grain) 

69 

1.5 

no  cracks 

_ 

70 

1.8 

0.83 

0.43 

0.46 

6.8x10’ 

2xl0'> 

43 

1.8 

0.95 

0.40 

0.53 

6.84x10’ 

2.09x10'’ 

55 

(1.8) 

1.39 

0.89 

0.77 

4.83x10’ 

1.47x10“ 

47 

2.6 

1.68 

1.30 

0.65 

1.57x10* 

1.44x10“ 

65* 

2.8 

1.95 

1.32 

0.70 

3.90x10’ 

4.48x10“ 

60 

2.9 

1.28 

0.70 

0.44 

1.03x10’ 

0.13 

77 

3.2 

1.92 

0.99 

0.60 

6.16x10* 

0.10 

63 

3.2 

1.29 

0.90 

0.40 

1.53x10* 

2.58x10“ 

74 

3.2 

1.87 

1.28 

0.58 

8.05x10* 

0.27 

75 

3.2 

1.95 

0.96 

0.61 

4.83x10* 

8.53x10“ 

64 

3.3 

1.14 

0.70 

0.35 

2.38x10* 

4.36x10“ 

44 

3.3 

1.77 

1.14 

0.54 

6.71x10* 

0.125 

61 

3.4 

1.26 

0.86 

0.37 

1.76x10* 

3.59x10“ 

76 

3.5 

1.66 

0.89 

0.47 

4.50x10* 

0.10 

78 

3.5 

2.28 

2.94 

0.65 

5.30x10* 

0.12 

49* 

3.5 

1.18 

0.60 

0.34 

1.95x10’ 

0.434 

56* 

4.2 

1.15 

0.61 

0.27 

1.30x10’ 

0.523 

62 

4.7 

2.09 

1.36 

0.44 

4.26x10’ 

2.53 

57 

4.8 

2.85 

2.66 

0.59 

*.  03x10* 

0.23 

72 

4.8 

3.8 

2.05 

0.79 

1.76x10’ 

1.03 

58 

5.2 

2.51 

1.48 

0.48 

4.20x10* 

0.30 

73 

5.4 

2.45 

1.56 

0.45 

1.83x10’ 

0.80 

59 

5.5 

3.85 

1.45 

0.70 

3.18x10’ 

2.27x10“ 

71 

5.5 

3.38 

2.33 

0.61 

1.28x10’ 

1.13 

79 

6.0 

3.83 

1.78 

0.64 

— 

— 

•  Grain  size  achieved  by  grain  growth  process. 


a.  Number  of  cracks  per  cubic  meter. 

Figure  12.  Crack  density  vs  grain  diameter.  Axial  strain 
levels  are  indicated. 


CO 

sO 


b.  Number  of  cracks  per  grain. 

Figure  12  (cont’d).  Crack  density  vs  grain  diameter.  Axial 
strain  levels  are  indicated. 


comparing  the  results  with  those  of  the  usual 
cracks-per-unit-volume  method  discussed  earlier. 
For  specimen  71,  the  thick  section  analysis  gave  a 
crack  density  of  1.13  cracks  per  grain  and  the  thin 
section  analysis  gave  0.92  crack  per  grain,  indicat¬ 
ing  a  reasonable  agreement  for  the  existing  condi¬ 
tions. 

Additionally,  some  observations  were  made 
from  thick  section  photographs  taken  parallel  to 
the  stress  axis.  These  provided  information  on  the 
shape  of  the  cracks  and  their  orientation  to  the 
stress  axis. 

Creep  behavior 

Figure  14  shows  some  representative  strain-time 
plots  for  tests  at  2.0  MPa.  Figures  15a-c  show 
creep  rate  vs  axial  strain  for  all  tests  conducted  at 
2.0-MPa  axial  stress.  Figures  15d-f  show  similar 
plots  of  the  results  of  tests  subjected  to  the  higher 
stress  levels  (2.4, 2.6  and  2.8  MPa).  The  strain  rate 
minima  show  up  clearly  when  the  data  are  plotted 
in  this  manner.  Note  that  the  scale  of  the  strain 


axes  varies  to  accommodate  the  range  of  strain 
found  in  the  different  tests. 

Most  specimens  tested  to  sufficiently  high 
strains  exhibit  typical  creep  behavior.  The  larger 
grain-sized  material  generally  showed  a  rapidly  de¬ 
creasing  primary  creep  rate,  a  brief  minimum  and 
a  tertiary  phase  in  which  the  creep  rate  tended  to  a 
constant  at  higher  strains. 

The  smaller-grained  material  often  showed  a 
brief  period  of  increasing  creep  rate  at  very  low 
strains.  The  primary  creep  rate  reached  a  maxi¬ 
mum  in  the  range  of  10'5  to  2  x  10"’  strain  and  then 
decreased,  developing  a  relatively  broad  minimum 
near  10'1  axial  strain. 

Several  specimens  were  tested  at  stresses  of  2.4, 
2.6  and  2.8  MPa  in  order  to  examine  the  effect  of 
axial  stress  on  the  cracking  activity  over  a  limited 
range.  Creep  data  for  these  tests  are  plotted  in  Fig¬ 
ures  lSd  and  15c.  No  strong  trends  emerge  from 
the  results  of  these  tests.  Results  given  in  Table  4 
show  that  no  significant  changes  occur  in  the  nor¬ 
malized  crack  size,  indicating  that  the  stress  level 


v; 


‘>1 


$ 

£4 


'.V, 

t.'r, 

r.v, 

f.V 

& 


x-: 


/ 


«r.  ert 


AV-V-V-V-V-V* 


.  ■%. 
>:-i 

V  \ 


22 


a.  Specimens  tested  to  large  strains. 


b.  Some  specimens  tested  to  strains  of  0.25  x  10~2  and 
0.5x10 


c.  Specimens  tested  to  strains  of  approximately  10'2. 


Figure  15.  Creep  curves  for  all  tests. 


d.  Some  specimens  strained  to  approximately  l O'1  under  vari¬ 
ous  stresses. 


e.  Additional  specimens  tested  to  strains  of  approximately 
10  '  under  various  stresses. 


Figure  15  (cont'd). 


/.  Specimens  experiencing  grain  growth  prior  to  testing. 


Figure  15  (cont ’d).  Creep  curves  for  all  tests. 


Figure  16.  Minimum  creep  rate  vs  grain  diam¬ 
eter,  o-2  MPa. 


does  not  affect  the  crack  size  -  grain  size  relation¬ 
ship  over  this  range. 

Although  there  is  scatter  in  the  creep  results,  the 
minimum  strain  rate  increases  with  increasing 
stress.  Inspection  of  the  results  given  in  Table  4  in¬ 
dicates  that  the  number  of  cracks  per  unit  volume 
generally  increases  with  stress  as  well.  The  maxi¬ 
mum  fracture  rate  with  respect  to  time  has  a  mild 
tendency  to  occur  at  lower  strains  as  stress  increas¬ 
es. 

Figure  15f  shows  the  creep  curves  of  three  speci¬ 
mens  for  which  a  relatively  large  grain  size  was 
achieved  through  a  grain  growth  process.  These 
specimens  remained  at  a  temperature  of  -2  °C  for 


a  number  of  weeks  and  consequently  experienced 
considerable  grain  growth.  Upon  testing,  they  ex¬ 
hibited  significantly  different  creep  characteristics 
from  the  other  specimens,  developing  no  decel¬ 
erating  primary  creep  phase.  This  phenomenon  is 
discussed  in  the  section  entitled  The  Effect  of 
Grain  Growth. 

Table  1  gives  the  minimum  creep  rates  along 
with  other  information.  The  creep  rate  minima  are 
plotted  in  Figure  16  as  a  function  of  grain  size. 

Table  1  jpves  the  strain  at  which  the  creep  rate 
minimum  e„.  occurred.  Figure  17  shows  the  strain 
at  lm„  as  a  function  of  grain  size  for  these  tests. 
Note  the  sharp  decrease  in  strain  level  with  in¬ 
creasing  grain  size,  indicating  the  loss  of  ductility 
with  increasing  grain  size. 

Crack  healing 

Observations  were  made  on  two  thick  sections 
to  ascertain  the  extent  to  which  crack  healing 
might  influence  the  crack  length  observations.  Fig¬ 
ures  18  and  19  show  two  sequences  of  time  lapse 
photographs  of  the  crack  healing  process.  The  sec¬ 
tions  were  stored  at  -5  °C  and  photographed  peri¬ 
odically.  Figure  18  shows  an  approximately  3-mm 
crack  face  on.  The  time  after  testing  for  each 
frame  is  given  in  the  figure.  Note  the  prominent 
surface  relief  of  the  crack  face.  Instead  of  a  smooth 
planar  surface,  the  crack  face  appears  to  be  com¬ 
posed  of  many  facets  as  indicated  by  the  network 
of  shadow  lines.  These  features  fade  rapidly  as  the 
crack  heals.  The  crack  surface  becomes  smooth 
and  the  void  is  gradually  transformed  into  a  “bub¬ 
ble”  having  the  shape  of  an  oblate  spheroid.  Fig- 


26 


Figure  17.  Strain  at  minimum  creep  rate  vs  grain  diameter  for  10  specimens. 


ure  19  shows  several  cracks  edge-on.  The  time  se¬ 
quence  is  the  same  as  for  Figure  18.  The  largest 
crack  did  not  heal  appreciably.  The  reason  is  that 
this  void,  unlike  the  others  studied,  was  exposed 
to  the  atmosphere  and  was  thus  filled  with  air.  As 
discussed  in  greater  detail  below,  this  changes  the 
rate  of  the  healing  process  significantly.  Figure  20 
shows  the  measured  crack  lengths  as  a  function  of 
time. 

Slip  plane  length  distribution 

Initially,  several  methods  of  obtaining  a  distri¬ 
bution  for  t,  the  length  of  slip  plane,  based  on 
ideal  grain  geometries  were  considered.  These 
proved  somewhat  unrealistic  in  light  of  the  differ¬ 
ences  between,  say,  an  idealized  circular  or  hexa¬ 
gonal  cross  section  and  the  variety  of  shapes  actu¬ 
ally  observed  in  the  material  (see  thin-section  pho¬ 
tographs,  for  example).  In  order  to  obtain  a  more 
realistic  sampling  of  slip  line  lengths,  the  follow¬ 
ing  method  was  devised.  A  straight  edge  was  placed 
on  a  thin-section  photograph  and  the  distance  be¬ 
tween  the  grain  boundaries  thus  intersected  was 
recorded  as  the  slip  plane  length.  This  was  done 
several  times  on  each  photograph  and  for  photo¬ 
graphs  from  five  specimens  of  varying  grain  size. 
In  all,  419  measurements  were  taken.  The  values 
from  each  specimen  were  normalized  to  the  speci¬ 
men  grain  diameter,  allowing  all  points  to  be 
merged.  Nearly  10%  of  the  values  were  greater 
than  1.0,  indicating  that  several  of  the  potential 
slip  planes  encountered  were  larger  than  the  aver¬ 
age  grain  size.  This  is  to  be  expected  since  the 


grains  are  not  exactly  uniform  in  size.  The  mean 
and  standard  deviation  of  the  normalized  slip 
plane  lengths  are  0.6  and  0.3.  Figure  21  shows  the 
distribution  of  slip  plane  lengths.  Note  that  the 
maximum  length  is  1.5 d.  The  mean  value  of  Q.6d 
is  used  throughout  this  work  when  an  “average” 
slip  plane  length  is  required. 

Acoustic  emission  observations 

Figure  22  shows  typical  AE  results.  Figure  22a 
gives  accumulated  events  versus  axial  strain.  The 
events  are  normalized  to  unit  volume.  The  curve 
exhibits  the  same  shape  seen  in  other  work  (i.e.  St. 
Lawrence  and  Cole  1982)  but  given  the  filtering 
process  used  in  the  present  work,  the  curve  is  in¬ 
dicative  of  the  actual  number  of  fractures  occur¬ 
ring  per  unit  volume.  Figure  22b  shows  the  deriva¬ 
tive  of  the  curve  in  Figure  22a.  Note  that  most  of 
the  fracturing  activity  occurs  at  very  low  strains. 
Table  5  summarizes  the  AE  data;  it  contains  only 
results  from  specimens  for  which  adequate  AE  data 
were  obtained.  In  certain  cases  technical  problems 
occurred  in  the  recording  of  the  AE  data,  which 
prevented  subsequent  analysis.  In  other  cases  ap¬ 
parently  inadequate  specimen-transducer  contact 
caused  the  results  to  be  of  questionable  validity. 

The  onset  of  fracturing,  as  indicated  by  the  AE 
results,  occurred  at  an  average  axial  strain  of 
4.7  x  10  *  with  a  standard  deviation  of  4.3  x  10  *. 
The  maximum  fracturing  rate  with  respect  to 
strain,  [dAE/de]„„,  occurred  at  1.95x10"’  axial 
strain  with  a  standard  deviation  of  9.6x10'*.  The 
maximum  fracturing  rate  with  respect  to  time, 


f 

t 

/ 

i 

f 


f 

t 

t 

«* 

! 


c\  240  hours.  d.  1296  hours. 

Figure  18.  Time-lapse  photographs  of  crack  healing,  face  view. 


\dAE/dt)„a,,  occurred  a!  an  axial  strain  of 
1.75  x  10-’  with  a  standard  deviation  of  8.8  x  10'*. 
These  maximum  rate  calculations  unit  specimen 
59,  which  did  not  experience  sufficiently  high 
strains  to  exhibit  a  plausible  maximum.  There  ap¬ 
pears  to  be  no  systematic  relationship  between  the 
strain  at  the  fracturing  onset  and  grain  size. 

Figure  23  shows  the  effect  of  grain  size  on  the 
time  to  the  maximum  fracturing  rates  with  respect 
to  strain  and  time  for  the  2.0-MPa  tests.  The  time 
to  the  rate  maxima  shows  a  strong  dependency  on 
grain  size,  decreasing  roughly  an  order  of  magni¬ 
tude  as  grain  size  increases  from  1.8  to  5.5  mm. 


Table  5  also  gives  the  AE  amplitude  filter 
threshold  and  the  average  amplitude  of  the  filtered 
events.  The  mean  of  the  filtering  threshold  for  all 
the  tests  is  83.7  dB  with  a  standard  deviation  of 
4.7  dB. 

Grain  orientation 

A  number  of  grain  orientation  measurements 
were  made  to  discern  any  trends  in  the  orientation 
of  grains  having  internal  cracks.  Two  thin  sections 
prepared  from  specimen  79  were  examined  in  de¬ 
tail.  The  thin  sections  contained  numerous  grain 
boundary  and  transgranular  cracks.  The  c-axis 


28 


272x3 


IAE/m 


040  080 

Amal  Strain 


040  080 

Axial  Strain 


a.  Accumulated  acoustic  events  per  cubic  meter 
vj  axial  strain. 


b.  Acoustic  events  per  unit  strain  vs  axial  strain. 


Figure  22.  Typical  acoustic  emission  data. 


Table  5.  Results  of  acoustic  emission  observations. 


AE  rale  maximum 


AE  rate  maximum 


Specimen 

AE  filter 

A  verage 

S/d.  dev. 
(dB) 

First  event 

(with  respect  to  strain ) 

(with  respect  to  time) 

threshold 

(dB) 

amplitude 

(dB) 

€ 

( Xio v 

l 

(S) 

[dAE/dcJm<u 

< 

(xlO1) 

/ 

(S) 

[dAE/dt]max 

(s-') 

e 

(xlO7) 

/ 

(S) 

43 

78.5 

82.2 

2.7 

7.07 

16.0 

3.26x10* 

0.252 

330 

1.58x10' 

0.252 

330 

44 

83.9 

87.9 

3.2 

9.6 

15.0 

1.85x10* 

0.329 

195 

2.30x10’ 

0.225 

105 

47 

— 

— 

— 

0.14 

16.7 

6.57x10* 

0.124 

300 

2.82x10' 

0.088 

210 

49 

76.6 

86.2 

4.1 

0.10 

0.6 

4.03  x  10* 

0.240 

60 

— 

— 

S3 

75.5 

83.7 

3.9 

2.69 

15.3 

5.89x10* 

0.237 

420 

2.26x10' 

0.237 

420 

56 

85.7 

87.8 

1.4 

— 

1.0 

1.16x10'° 

0.312 

150 

5.45x10* 

0.312 

150 

58 

88.0 

90.0 

1.3 

3.6 

9.4 

1.39x10’ 

0.104 

51 

1.41  10’ 

0.104 

51 

59* 

87.5 

89.8 

1.6 

1.15 

7.8 

9.33  x  10* 

0.0417 

39 

8.33x10' 

— 

— 

63 

81.6 

86.1 

2.6 

0.60 

3.9 

9.38x10* 

0.125 

150 

4.59x10’ 

0.125 

150 

65 

88.7 

90.0 

0.94 

at  start 

— 

8.05  x 10* 

0.264 

105 

1.16x10’ 

0.264 

105 

70 

74.8 

81.8 

4.3 

0.24 

5.3 

2.24x10* 

0.16 

380 

9.30x10' 

0.129 

300 

73 

86.8 

89.2 

1.4 

9.8 

7.1 

1.85x10’ 

0.19 

150 

1.12x10’ 

0.152 

90 

74 

87.3 

87.3 

2.7 

9.6 

2.1 

7.23x10’ 

0.30 

60 

8.61  x 10* 

0.30 

60 

75 

87.3 

89.2 

1.2 

5.9 

0.6 

3.27x10’ 

0.209 

90 

1.95x10’ 

0.179 

60 

76 

86.2 

88.1 

1.3 

1.15 

16.5 

1.01  x  10° 

0.0147 

60 

2.41  x  10’ 

0.0147 

60 

77 

85.6 

87.4 

1.3 

10.4 

16.5 

1.28x10’ 

0.301 

90 

2.96x10' 

(0.16) 

(  30) 

78 

85.3 

87.6 

1.4 

3.0 

18.3 

1 .65  x  10* 

0.116 

90 

1.91  x 10’ 

0.077 

60 

Specimen  not  tested  to  sufficiently  high  strain  to  develop  an  obvious  maximum  AE  rate. 


a.  Time  to  (dAE/dtJmi,,  vs  grain  size. 


0  2  4  6 


<1  (mm) 

b.  Time  to  [dAE/dl]„a,  vs  grain  size. 

Figure  23.  Acoustic  emission  rate  data. 

orientations  of  selected  clusters  of  grains  were  de¬ 
termined  using  a  universal  stage  according  to 
methods  given  by  Langway  (1958),  and  using  a 
correction  factor  of  1.04  on  the  equatorial  meas¬ 
urements  rather  than  the  tabulated  values  (see 
Kamb  1962).  Appendix  B  gives  the  results  of  these 
measurements. 

The  results  of  measurements  on  all  grains,  both 
those  containing  cracks  and  the  adjacent  uncracked 
grains,  reflect  the  random  orientation  of  the  test 
material.  No  pattern  of  preferred  orientation  of 
these  grains  emerges.  A  fabric  diagram  for  only 
the  grains  containing  cracks  also  yields  no  discern¬ 
ible  pattern. 

An  examination  of  the  relative  orientation  of 
two  grains  having  a  crack  along  their  common 
grain  boundary  revealed  that  the  angle  between 
the  respective  c-axes  ranges  from  33°  to  85°,  with 
a  mean  of  63.3°  and  a  standard  deviation  of  19°. 

The  above  results  are  not  unexpected,  however, 
since  it  is  the  grains  that  contain  the  active  slip  sys¬ 
tems,  and  not  the  cracked  grains,  where  one  would 


expect  to  find  a  preferred  orientation.  As  noted  in 
an  earlier  section,  the  grains  most  likely  to  slip  and 
thus  cause  crack  nucleation  will  tend  to  have  ori¬ 
entations  that  maximize  the  shear  stress  on  their 
basal  planes.  Unfortunately,  it  was  not  possible  to 
determine  which  grains  were  important  in  forming 
the  observed  cracks.  In  all  probability,  the  grains 
that  generated  the  stress  concentration  were  not 
even  in  the  thin  section. 

Theseresultsalsoindicate  that  the  cracks  formed 
on  planes  other  than  the  basal  in  grains  containing 
transgranular  cracks.  Some  grains  were  observed 
to  have  cracks  running  roughly  parallel  to  the 
c-axis. 


ANALYSIS  AND  DISCUSSION 

As  the  previous  section  shows,  the  results  of  the 
testing  program  provide  information  on  a  consid¬ 
erable  range  of  topics  relative  to  the  response  of 
ice  to  uniaxial  compressive  loading.  These  topics, 
which  are  discussed  in  this  section,  may  be  briefly 
summarized  as  follows. 

1)  Crack  length.  The  average  crack  length  scales 
linearly  with  the  average  grain  size. 

2)  Crack  density.  The  number  of  cracks  per  unit 
volume  increases  with  grain  size  for  the  stated  con¬ 
ditions. 

3)  Onset  of  cracking.  The  test  material  showed  a 
transition  from  ductile  flow  with  no  cracking  to 
flow  with  a  considerable  degree  of  cracking  as  the 
grain  size  increased  from  1.5  to  5.7  mm. 

4)  Creep  behavior.  Grain  size  affected  creep  be¬ 
havior  significantly.  As  grain  size  increased,  pri¬ 
mary  and  tertiary  creep  rates  increased  and  the 
strain  at  the  minimum  creep  rate  decreased  signifi¬ 
cantly. 

5)  Crack  healing.  Observations  indicate  that  iso¬ 
lated,  vapor-filled  cracks  undergo  a  fairly  rapid 
healing  process  which  eventually  transforms  them 
into  a  bubble-like  cavity.  Air-filled  cracks  undergo 
healing  at  a  significantly  slower  rate. 

6)  Stress  effects.  Test  results  at  somewhat  higher 
stresses  indicate  that  the  crack  density  increased 
with  stress,  but  that  the  size  of  the  forming  cracks 
was  not  affected  by  the  stress  level. 

7)  Crack  location  and  grain  orientation.  Cracks 
formed  either  at  grain  boundaries  or  across  grains 
with  nearly  equal  probability,  and  the  grains  that 
developed  cracks  exhibited  no  preferred  orienta¬ 
tion  to  the  stress  axis. 

8)  Acoustic  emission  activity.  All  specimens 
emitted  considerable  acoustic  activity.  Visible 
cracks  generated  the  highest  amplitude  events  and 


the  observations  permitted  some  progress  toward 
establishing  an  event  amplitude  level  associated 
with  the  formation  of  a  visible  microcrack. 

This  section  deals  with  the  above  points  and  ad¬ 
dresses  the  effect  of  the  measurement  techniques 
on  the  results  as  well  as  the  level  of  uncertainty  in 
the  results. 

Thick  section  observations 

The  estimation  of  the  size  and  number  of  cracks 
in  the  thick  sections  proved  to  be  a  very  tedious 
process.  Specimens  with  a  relatively  high  crack 
density  were  difficult  to  analyze  from  the  photo¬ 
graphs  alone  (see,  for  example  Fig.  11a).  In  order 
to  improve  accuracy,  it  was  sometimes  necessary 
to  record  the  number  of  cracks  in  each  sector  of 
the  thick  section  at  the  time  the  photograph  was 
taken,  as  well  as  note  some  general  observations 
about  the  network  of  cracks.  This  additional  in¬ 
formation  greatly  improved  the  reliability  of  the 
measurements. 

Since  an  observer’s  acuity  in  this  type  of  task  is 
likely  to  improve  with  experience,  all  the  crack 


counts  and  measurements  were  carried  out  twice. 
In  some  cases  (most  notably  specimens  49  and  55), 
the  photographs  were  of  relatively  poor  quality 
and  thus  these  results  should  be  treated  with  some 
caution. 

Most  specimens  having  low  or  intermediate 
crack  densities  (less  than  approximately  0.5  crack 
per  grain)  displayed  relatively  unambiguous  net¬ 
works  of  cracks  when  photographed.  The  cracks 
were  isolated  and  were  thus  easily  identified  and 
measured.  The  photograph  in  Figure  lib  shows  a 
typical  sector  from  the  thick  section  of  specimen 
44.  As  noted  earlier,  highly  cracked  specimens 
were  evaluated  by  using  thin  sections.  Additional¬ 
ly,  a  careful  examination  of  the  size  and  number 
of  cracks  which  would  appear  ambiguous  in  the 
thick  section  photographs  provided  information 
which  helped  improve  the  reliability  of  the  results. 

As  noted  above,  thick  sections  taken  parallel  to 
the  axis  of  stress  were  not  suitable  for  crack  densi¬ 
ty  measurements  since  it  was  difficult  to  identify 
individual  cracks  in  that  plane  of  observation.  Fig¬ 
ure  24  shows  a  photograph  of  a  typical  tested  spec- 


Figure  24.  Thick  section  photograph  taken  parallel  to  the  axis  of  applied  stress. 


34 


and  plane  of  crock 


Figure  25.  Distribution  of  the  angle  be¬ 
tween  the  axis  of  compressive  stress  and 
the  plane  of  the  observed  crack  (40  obser¬ 
vations). 


imen.  It  is  a  thick  section  of  material  near  the  cen¬ 
ter  of  the  specimen  and  it  shows  several  cracks 
face-on  or  nearly  so.  When  viewed  from  this 
angle,  the  cracks  near  the  surface  mask  those 
deeper  in  the  section,  making  an  accurate  count 
nearly  impossible.  However,  this  type  of  photo¬ 
graph  is  useful  in  that  it  shows  the  general  shape 
of  the  cracks  and  it  also  provides  a  means  of  esti¬ 
mating  the  orientation  of  the  plane  in  which  the 
crack  forms  relative  to  the  axis  of  applied  stress. 

Reliable  measurements  of  this  angle  can  be 
made  only  on  cracks  that  appear  edge-on  in  the 
photograph.  Consequently,  relatively  few  meas¬ 
urements  were  available  since  only  several  repre¬ 
sentative  photographs  of  these  vertically  oriented 
thick  sections  were  taken.  Figure  25  shows  the 
results  of  40  observations  in  the  form  of  a  histo¬ 
gram.  Note  that  the  cracks  tend  to  cluster  about 
the  vertical  plane.  The  average  angle  is  23 0  with  a 
standard  deviation  of  17.5°.  Ninety  percent  of  the 
observations  fall  within  45°  of  the  stress  axis. 

Interestingly,  a  few  cracks  formed  at  a  relatively 
large  angle  to  the  stress  axis  and  one  crack  formed 
nearly  perpendicular  to  it. 

The  grain  size  vs  crack  size  relationship 

This  section  examines  the  results  of  the  crack 
length  observations  and  addresses  the  errors  intro¬ 
duced  by  the  observational  method  and  crack 
healing.  Quantification  of  the  sources  of  error 
provides  a  means  of  studying  their  effect  on  the  re¬ 
sults.  Initially,  a  theoretical  grain  size  vs  crack  size 
relationship  is  developed;  later  this  relationship  is 
compared  to  the  experimental  results. 


The  relationship  between  grain  size 
and  nucleated  crack  size 
This  section  develops  a  relationship  between 
grain  size  and  nucleated  crack  size  by  using  the 
concepts  of  elastic  strain  energy  and  surface 
energy.  It  is  similar  to  the  approach  of  Gold  (1966) 
except  that  the  strain  energy  term  considers  the 
pileup  as  a  superdislocation  and  no  flaw  exists  un¬ 
til  the  instant  of  nucleation.  The  method  relies  on 
the  assumption  that  all  the  strain  energy  associ¬ 
ated  with  the  pileup  goes  to  form  new  surface  area 
when  the  crack  forms.  There  is  also  some  inherent 
inaccuracy  because  the  expression  used  for  strain 
energy  was  developed  for  the  isotropic  elastic  case. 
Additionally,  it  is  recognized  that  the  results  of 
such  an  analysis  are  a  strong  function  of  the  values 
assumed  for  various  geometric  parameters  such  as 
obstacle  spacing  and  the  width  of  the  slip  plane. 
The  values  used  here  are  in  agreement  with  those 
found  in  the  literature  (e.g.  Gold  1966)  and  no  at¬ 
tempt  has  been  made  to  obtain  a  range  of  values 
or  a  distribution  to  represent  such  quantities,  with 
the  exception  of  the  slip  plane  length. 

The  calculations  are  based  on  a  grain  diameter 
of  2  mm.  A  slip  plane  length  of  (  =  0.6 d  =  1.2 
mm  is  used  as  a  representative  value.  This  comes 
from  using  the  average  value  of  the  normalized 
slip  plane  length  distribution,  which  was  discussed 
in  a  previous  section.  Only  basal  slip  is  considered 
in  this  treatment.  It  is  also  assumed  that  the  dislo¬ 
cation  pileup  extends  across  a  grain  on  the  slip 
plane  so  the  pileup  length  is  equivalent  to  the  slip 
plane  length. 

Using  eq  12  with 

7  =  0.109  J  m'2  (average  surface  ener¬ 
gy  from  Hobbs  1974) 
g  =  3.5  GPa  (Hobbs  1974) 
t  =  1.2x10-’  m 
0  =  70.50° 
v  =  0.33 

the  resulting  nucleation  stress  is 
o.  =  1.05  MPa. 

When  eq  13  is  used  with  b  =  4.52x10  m,  the 
number  of  dislocations  causing  nucleation  is 

n  =  1200. 


Now  the  elastic  strain  energy  of  n  dislocations  in 
a  pileup  is  given  by  Hirth  and  Lothe  (1968)  as 


L  fijnb) 

4 7r(  I  -  r) 


4 R 

( 


(21a) 


35 


where  (  =  length  of  dislocation  pileup  (slip  plane 
length) 

L  =  length  of  dislocation  line 

R  =  half  obstacle  spacing. 

Assuming  that  L  =  d,  i.e.  the  slip  line  extends 
across  the  grain,  that  f  =  0.6 d  (the  average  of  the 
slip  plane  length  distribution)  and  that  R  =  0.5 d, 
the  energy  of  the  pileup  is  found  to  be 

W  =  2.9  xlO'7  J. 

To  a  first  approximation,  if  the  crack  is  assumed 
to  be  circular,  it  will  have  area  A  =  iry/V4  where 
y'  is  the  calculated  crack  size.  The  nucleated  crack 
has  1A  of  new  surface  area.  The  energy  required 
to  generate  this  area  is  7(2/1).  If  the  elastic  energy 
of  the  pileup  is  equated  to  the  energy  required  for 
generating  surface  area, 

fV  =  7(2/1)  (21b) 

it  is  seen  that 

A  =  (W/2y)  =  1.33xlO-‘  mJ 
or 

yj  =  1.30x10-’  m. 

Thus,  a  crack  size  of  1.30  mm  results  on  average 
for  2.0  mm  grain  size  material  when  it  is  subjected 
to  sufficient  stress  to  nucleate  cracks.  The  ratio  of 
crack  size  to  grain  size  in  this  case  is  0.65.  A  plot 
of  this  relationship  (see  Fig.  10)  indicates  the  lin¬ 
ear  relationship  between  grain  size  and  nucleated 
crack  size. 

Since  in  the  above  analysis  the  crack  size  goes  to 
zero  as  grain  size  goes  to  zero,  and  the  ratio  of  0.65 
may  be  interpreted  as  the  slope  of  the  relationship 
between  the  two  variables,  the  theoretical  relation 
between  crack  size  and  grain  size  may  be  written  as 

y.'  =  0.65  d.  (22) 

where  y.'  is  crack  size  (mm)  and  d  -  grain  di¬ 
ameter. 

Note  that  the  above  treatment  assumes  crack 
formation  a!  all  grain  sizes.  Since  this  is  clearly  not 
the  case,  a  crack  nucleation  criterion  must  be  ap¬ 
plied  to  determine  the  threshold  grain  size  for  nu¬ 
cleation,  and  thus  establish  a  lower  limit  to  eq  22. 

Note  that  the  crack  nucleation  theory  examined 
in  an  earlier  section  (eq  12)  provides  a  means  to  es¬ 
tablish  this  threshold  grain  size  for  crack  nuclca- 
tion. 


Observed  crack  length 
and  sources  of  error 

As  noted  earlier.  Figure  10  shows  the  result  of 
the  crack  size  measurements  for  all  tests  along 
with  the  best  fit  line  using  the  linear  regression 
technique.  The  equation  for  this  line  (r1  =  0.75)  is 

y.  =  -  0.44  +  0.67 d.  (23) 

Equation  22,  the  theoretical  prediction,  is  also 
plotted  in  Figure  10.  Note  that  the  test  results  ex¬ 
hibit  the  linearity  predicted  by  the  model.  Interest¬ 
ingly,  the  theory  predicts  nearly  the  same  slope 
found  in  the  regression  equation,  but  the  curve  is 
shifted  to  somewhat  higher  crack  sizes  throughout 
the  range  of  grain  size. 

The  overprediction  of  the  model  probably  stems 
in  part  from  its  simplicity.  It  is  likely  that  energy  is 
exnended  in  overcoming  the  compressive  back¬ 
ground  stress  in  addition  to  creating  new  surface 
area.  This  would  tend  to  decrease  the  resulting 
crack  size  prediction.  Additionally,  failure  of  the 
crack  formation  event  to  dissipate  all  the  available 
strain  energy  could  contribute  to  the  observed  dis¬ 
parity.  In  fact,  this  circumstance  would  help  ex¬ 
plain  the  difference  in  x-intercept  between  the 
theoretical  and  actual  results.  In  this  case,  equa¬ 
tion  21b  would  take  the  form 

W  =  7(2  A)  +  W„  (24) 

where  W„  is  the  residual  strain  energy  after  forma¬ 
tion  of  the  crack.  The  net  effect  would  be  a  de¬ 
crease  in  crack  size  for  a  given  grain  size  and  a 
shift  in  the  x-intercept  from  the  origin  to  some 
small  grain  size. 

Although  this  potential  source  of  error  in  the 
modeling  will  not  be  addressed  further,  two  sourc¬ 
es  of  error  in  the  crack  length  measuring  process 
require  special  attention,  namely  the  effects  of 
crack  healing  and  the  method  of  crack  length 
measurement  on  the  observed  crack  lengths. 

Crack  healing.  When  a  crack  forms,  it  immedi¬ 
ately  begins  to  heal.  This  is  a  result  of  the  thermo¬ 
dynamic  instability  associated  with  the  crack 
geometry.  The  edges  of  the  cracks  have  an  ex¬ 
tremely  small  radius  of  curvature  and  the  crack 
faces  have  a  relatively  large  radius  of  curvature. 
When  the  crack  remains  isolated  from  the  atmos¬ 
phere  after  its  formation,  it  quickly  fills  with 
water  vapor  in  an  attempt  to  reach  equilibrium. 
However,  the  large  differences  in  surface  curva¬ 
ture  within  the  crack  must  be  eliminated  before 
equilibrium  can  be  achieved. 

Equilibrium  results  when  there  is  no  pressure 
difference  between  the  ice  and  vapor  phases  at  all 


36 


points  on  the  interface.  This  is  clearly  not  the  cas’ 
in  a  newly  formed  crack.  The  variations  in  the  ra¬ 
dius  of  curvature  result  in  variations  in  the  pres¬ 
sure  difference  between  the  two  phases  along  the 
crack  surface  (see  Colbeck  1980).  The  pressure 
difference  variation  drives  a  flow  process  whereby 
material  is  transported  from  regions  of  low  curva¬ 
ture  to  regions  of  high  curvatun  .  This  process 
gradually  brings  the  void  into  a  nominally  spheri¬ 
cal  shape  with  a  relatively  constant  radius  of  curv¬ 
ature.  The  rate  of  the  process  decreases  as  the  dif¬ 
ference  in  curvature  decreases. 

In  the  present  case  of  an  isolated  crack,  the  void 
contains  only  water  vapor.  The  transport  mecha¬ 
nism  is  viscous  flow  in  the  vapor  phase,  which  is 
fast  relative  to  a  diffusion  process.  The  process 
that  the  ice  undergoes  is  sublimation  in  the  true 
sense  of  the  word,  in  that  it  consists  of  both  evap¬ 
oration  from  and  then  condensation  back  to  the 
solid  phase. 

If  the  crack  and  the  surrounding  ice  are  viewed 
as  a  closed  system  with  no  imposed  temperature 
gradient,  heat  must  flow  from  the  surface  of  the 
crack  receiving  material  to  the  surface  losing  ma¬ 
terial  in  order  for  the  sublimation  process  to  pro¬ 
ceed.  Colbeck  (1986)  points  out  that  this  heat  flow 
is  in  fact  the  rate-limiting  factor  in  the  healing  pro¬ 
cess  of  vapor- filled  cracks. 

Now,  if  the  crack  interior  contains  air,  either 
from  being  opened  to  the  atmosphere  or  from  in¬ 
tersecting  a  gas  bubble  upon  nucleation,  the  heal¬ 
ing  rate  is  slowed  considerably  because  the  trans¬ 
port  mechanism  changes  from  viscous  flow  to  dif- 
fusional  flow,  an  inherently  slower  process.  The 
rate  limiting  factor  is  not  heat  flow,  but  rather  the 
diffusional  process  by  which  water  vapor  travels 
from  the  source  surface  to  the  sink  surface.  Thus, 
the  presence  of  another  gas  in  the  void  results  in  a 
significant  retardation  of  the  sublimation  process. 
Consequently,  the  healing  rale  of  a  gas-filled 
crack  is  much  slower  than  that  of  a  crack  contain¬ 
ing  only  water  vapor  (see  Colbeck  1986  for  an  in- 
depth  treatment  of  this  topic).  The  large  crack  in 
the  center  of  the  photographs  in  Figures  19a-d 
was  filled  with  air  during  the  sectioning  process 
and  displayed  virtually  no  healing  during  the  ob¬ 
servation  period  (see  top  curve  in  Fig.  20b). 

The  question  at  hand  is  whether  this  crack-heal¬ 
ing  process  occurs  fast  enough  to  significantly  in¬ 
fluence  the  crack  length  measurements  taken  up  to 
several  hours  after  their  formation.  To  obtain  the 
answer  to  this  question,  a  set  of  measurements 
were  made  as  discussed  earlier  (refer  to  Fig. 
20a, b). 

Since  most  of  the  cracks  observed  in  these  expe¬ 
riments  are  isolated  within  the  specimens,  it  ap¬ 


pears  that  the  fast  healing  rates  associated  with  the 
vapor  diffusion  mechanism  should  be  considered. 
Considering  the  crack  size  vs  time  data,  the  initial 
healing  rate  is  evidently  not  a  strong  function  of 
initial  crack  size.  Over  the  first  24-hr  period  of  ob¬ 
servation,  the  crack  length  reduction  does  not  vary 
systematically  with  the  original  crack  length,  but 
shows  considerable  scatter  for  cracks  of  similar  in¬ 
itial  length.  This  scatter  is  probably  due  to  varia¬ 
tions  in  the  distance  between  faces  (the  width)  of 
the  individual  cracks.  A  “wide”  crack,  i.e.  one 
with  a  relatively  large  distance  between  opposite 
faces,  requires  transport  of  a  greater  volume  of 
material  to  reduce  its  length  a  given  amount  than  a 
narrow  or  sharp  crack.  If  the  vapor  transport 
mechanism  is  assumed  to  operate  at  nominally  the 
same  rate  for  both  wide  and  narrow  cracks,  the 
wider  cracks  would  require  more  time  to  heal  a 
given  amount. 

Since  crack  length  measurements  were  generally 
taken  less  than  4  hr  after  testing,  estimation  of  the 
maximum  amount  of  healing  likely  to  occur  dur¬ 
ing  this  time  interval  is  of  interest.  Some  healing 
could  have  occurred  during  the  tests,  and  thus  the 
average  amount  of  healing  after  5  hr  should  pro¬ 
vide  a  very  conservative  upper  bound  to  the  crack 
length  reduction. 

The  data  indicate  that,  on  the  average,  the 
measured  crack  length  decreases  by  approximately 
10%  of  the  original  length  in  the  first  5  hr  after 
testing.  However,  as  noted  above,  the  absolute  re¬ 
duction  in  length  due  to  healing  appears  to  be  rela¬ 
tively  independent  of  initial  crack  length,  espe¬ 
cially  at  low  elapsed  times.  This  implies  that  the 
crack  lengths  observed  at  a  fixed  time  after  forma¬ 
tion  require  the  addition  of  a  constant  as  the  ap¬ 
propriate  means  to  correct  for  the  effects  of  the 
healing  process.  The  average  amount  of  healing  in 
the  first  5  hr  after  formation  was  0.08  mm  and  this 
value  is  used  as  the  healing  correction  factor. 
Again,  there  are  large  variations  in  the  amount  of 
healing  of  individual  cracks  and  cracks  which  are 
not  isolated  from  the  atmosphere  will  have  a  negli¬ 
gible  healing  rate  over  this  time  interval. 

Since  the  crack  healing  phenomenon  is  a  peri¬ 
pheral  aspect  of  this  work,  the  complexities  of  the 
healing  process  prevent  an  in-depth  examination 
at  the  present  time.  There  are  many  questions  to 
be  answered  in  this  connection:  the  effect  on  heal¬ 
ing  of  crack  location  (i.e.  grain  boundary  or  intra¬ 
crystalline),  the  point  in  the  healing  process  at 
which  the  crack  becomes  insignificant  as  a  cause 
of  stress  concentration,  and  the  manner  in  which 
crack  size  and  shape  affect  the  healing  process. 

Crack  orientation  and  measured  length.  In  gen¬ 
eral,  the  reported  crack  lengths  are  the  longest  di- 


%  s 


•I* 


Eq.22 
(theoreticol  prediction) 


Eq.25 

// (corrected  best  fit 
/  to  dato) 


Mean  Grain  Diameter  (mm) 


Figure  26.  Theoretical  prediction  and  observed  relation¬ 
ship  (after  error  corrections )  for  the  average  crack  size/ 
grain  size  relationship. 


mensions  of  the  cracks  projected  on  a  plane  per¬ 
pendicular  to  the  long  axis  of  the  specimen.  Error 
can  result  if  this  projection  does  not  adequately  re¬ 
flect  the  true  maximum  crack  length.  To  assess 
this  error,  60  cracks  were  evaluated  from  thick 
sections  taken  parallel  to  the  long  axis  of  the  speci¬ 
men.  For  each  crack,  the  ratio  of  the  maximum  di¬ 
mension  to  the  dimension  projected  on  a  horizon¬ 
tal  plane  (which  corresponds  to  the  measurements 
taken  in  the  crack  length  analysis)  was  computed. 
The  minimum  value  of  this  ratio  is  one.  The  ratio 
increases  as  the  true  maximum  becomes  larger 
than  the  maximum  projected  length.  The  average 
of  the  ratio  was  1.12  with  a  standard  deviation  of 
0.19,  indicating  that  the  true  crack  lengths  average 
12%  greater  than  the  values  actually  measured. 

Effect  of  error  on  the  observations 

The  influence  of  the  healing  process  and  the 
method  of  crack  length  measurement  may  be  in¬ 
corporated  into  the  results  by  applying  the  appro¬ 
priate  corrections  to  the  regression  equation  (eq 
23)  which  represents  the  test  data. 

Using  the  conservative  estimate  of  5  hr  for  the 
elapsed  time  between  crack  formation  and  meas¬ 
urement,  the  crack  healing  data  indicate  that,  on 
average,  a  crack  heals  0.08  mm  in  this  period.  The 
regression  equation  may  then  be  corrected  by  add¬ 
ing  the  healing  correction  and  multiplying  the  re¬ 
sult  by  the  factor  1.12.  The  factor  1 .  12  corrects  for 
the  12%  difference  between  the  projected  crack 
length  actually  observed  and  the  true  maximum 
length.  Thus 

y?  =  fy, +0.08)  1.12 


where  y*  is  the  corrected  crack  length  and  yc  is  the 
observed  crack  length.  Substituting  the  expression 
for  yr  from  eq  23, 

y*  =  (  -  0.44  +  0.67d  +  0.08)  1.12 


y*  =  -  0.4  +  0.75 d.  (25) 

Figure  26  shows  the  predicted  relationship  (eq  22) 
plotted  along  with  eq  25,  which  is  the  observed  re¬ 
lationship  after  error  corrections. 

Although  the  corrected  curve  has  a  somewhat 
steeper  slope  than  the  theoretical  prediction,  as 
well  as  a  nonzero  y-intercept,  the  agreement  over 
the  indicated  range  in  grain  size  is  very  good. 

As  a  final  note  in  this  regard,  the  crack  length 
histograms  presented  (i.e.  App.  A)  consist  only  of 
the  uncorrected  observations.  The  effect  of  apply¬ 
ing  the  corrections  to  these  data  would  be  a  shift 
to  larger  crack  lengths  and  a  slight  increase  in  the 
range  or  spread  of  the  data. 

Crack  nucleation  condition 

The  results  show  that  under  the  prevailing  test 
conditions,  cracks  begin  to  nucleate  at  grain  sizes 
between  1.5  and  1.8  mm.  Recall  that  the  1.5-mm 
grain-sized  specimen  exhibited  no  cracking  and 
very  slight  cracking  was  observed  in  the  1.8-mm 
grained  specimen  (see  Table  1).  Thus  the  threshold 
grain  size  lor  crack  nucleation  lies  in  this  range  of 
grain  sizes. 


38 


Given  this  information,  then,  the  validity  of  the 
crack  nucleation  condition  (eq  12)  may  be  tested 
by  solving  for  the  slip  plane  length  and  substitut¬ 
ing  appropriate  values  for  the  various  elements  of 
the  relationship.  If  eq  12  adequately  represents  the 
mechanism  of  crack  nucleation,  the  resulting  criti¬ 
cal  slip  plane  length  for  crack  nucleation  should 
coincide  reasonably  well  with  the  observed  critical 
grain  size  for  crack  nucleation.  The  development 
of  this  correspondence  between  slip  plane  length 
and  grain  size,  as  noted  earlier,  relies  on  the 
assumption  that  shear  strain  propagates  via  slip 
planes  that  extend  completely  across  the  grains. 

The  following  expression  is  obtained  by  solving 
eq  12  for  the  critical  slip  plane  length,  t: 

f  1 

2(1  -v)al  F(4>)  • 

Values  for  y,  n  and  i>  given  earlier  are  used.  How¬ 
ever,  the  values  for  oL,  the  effective  shear  stress  re¬ 
quired  for  crack  nucleation,  and  the  geomet¬ 
rical  parameter,  require  some  discussion. 

Under  the  prevailing  test  conditions,  the  maxi¬ 
mum  resolved  shear  stress  aMKss,  which  occurs  on 
the  most  favorably  oriented  slip  plane,  is  the  axial 
stress  aA  multiplied  by  the  maximum  Schmid  fac¬ 
tor  m  or 

Omrss  —  Qa  •  m. 

Since  oA  =  2.0  MPa  and  the  highest  value  of  m 
is  0.5, 

&MRSS  —  1.0  MPa. 

Now  the  maximum  effective  shear  stress  aM£J,  is 
the  maximum  resolved  shear  stress  less  the  fric¬ 
tional  stress  component  a0,  or 

Omess  =  Omrss  ~  O0. 

a0  represents  the  lattice  resistance  to  dislocation 
movement  in  terms  of  shear  stress.  The  only 
source  for  a  value  of  a0  for  ice  prepared  in  the 
same  manner  as  in  this  work,  and  at  the  same  test 
temperature  of  -5°C,  is  Lim  (1983).  He  reported  a 
value  of  0.56  MPa  for  the  frictional  component  of 
stress,  in  terms  of  axial  stress,  for  polycrystalline 
ice  tested  in  tension  under  an  average  strain  rate  of 
9.4  xlO'7  s'1.  Since  the  present  work  deals  with 
shear  stress,  the  value  of  0.56  MPa  has  been  multi¬ 
plied  by  0.5  and  rounded  to  one  significant  figure, 
yielding  a  value  of  ct0  =  0.3  MPa  for  the  shear 


stress  required  to  overcome  lattice  resistance  to 
dislocation  movement.  The  direction  of  applied 
stress  is  assumed  to  exert  no  influence  on  the  fric¬ 
tional  stress  value. 

Thus,  the  value  of  the  maximum  effective  shear 
stress  ac  to  be  used  in  eq  24  is 

Oe  ~  Omrss  ~  <*o 

=  1.0  MPa  -  0.3  MPa 

or  a£  =  0.7  MPa. 

The  function 

F{<t>)  =  (5  +  2  cos  <t>  -  3cos2<£)/4 

given  by  Smith  and  Barnby  (1967)  provides  a 
means  of  making  the  nucleation  stress  a,  sensitive 
to  the  slip  plane/crack  plane  geometry.  In  his 
treatment,  Stroh  (1957),  as  noted  above,  calculat¬ 
ed  the  optimum  value  of  <t>  to  be  70.5  0  based  on 
the  normal  stress  distribution  associated  with  the 
pileup.  His  results  show  this  point  to  be  relatively 
well  defined.  That  is,  the  probability  of  develop¬ 
ing  a  crack  at  a  larger  or  smaller  angle  <t>  decreases 
sharply  as  the  angle  deviates  from  70.5°. 

By  considering  shear  stress,  Smith  and  Barnby 
(1967)  showed  that,  while  the  optimal  value  of 
70.5°  was  correct,  the  angle  <f>  can  vary  from  0°  to 
somewhat  over  90°  with  relatively  little  change  in 
the  stress  required  for  crack  nucleation.  This  re¬ 
sult  has  the  net  effect  of  making  the  stress  required 
for  nucleation  of  a  crack  less  sensitive  to  local 
geometric  factors. 

Considering  the  likely  range  in  <j>  to  be  0°  to  90°, 
the  minimum  and  maximum  values  of  F(<f>)  are  1 .0 
and  1.34.  These  values  occur  at  <t>  =  0°and  70.5°. 

It  is  now  possible  to  calculate  a  range  in  slip 
plane  lengths  over  which  crack  nucleation  is  possi¬ 
ble  given  the  prevailing  test  conditions.  Equation 
26  yields  the  following  values: 

F(<t>)  =  1.00,  (  =  1.8  mm 

F(0)  =  1.34,  f  =  1.4  mm. 

This  range  in  slip  plane  length  agrees  well  with  the 
range  in  grain  size  (1.5  to  1.8  mm)  over  which  the 
transition  from  no  cracking  to  cracking  was  ob¬ 
served.  Thus,  given  the  assumptions  mentioned 
above,  the  nucleation  criterion  (eq  12)  appears  to 
model  the  observed  ice  behavior  reasonably  well. 

The  fact  that  ice  has  a  relatively  low  coefficient 
of  self-diffusion  £>,  is  undoubtedly  a  major  factor 


39 


in  the  agreement  between  theory  and  observation 
in  this  case.  D,  for  icc  at  -10°C  (corresponding  to 
a  homologous  temperature  of  0.96)  is  on  the  order 
of  10'"  m!  s'1  (Hobbs  1974)  while  a  typical  value 
for  a  metal  is  on  the  order  of  10  "  m!  s'1 
(Shewmon  1969).  The  lower  capability  for  the  dif¬ 
fusion  of  vacancies  in  ice  enhances  the  material’s 
ability  to  build  and  sustain  the  stress  concentra¬ 
tions  necessary  for  the  nucleation  of  cracks  at  high 
homologous  temperatures.  In  contrast,  at  high  ho¬ 
mologous  temperatures  in  metals,  the  high  degree 
of  vacancy  diffusion  inhibits  pileup  formation  and 
thus  precludes  the  development  of  stress  concen¬ 
trations  necessary  for  crack  nucleation. 

Crack  density  and  specimen  strain 

It  is  useful  to  examine  the  cracking  activity  as  a 
function  of  strain.  The  results  given  in  Figure  13 
are  in  qualitative  agreement  with  the  work  of 
others  who  have  made  direct  observations  of  inter¬ 
nal  cracks  in  ice  (Gold  1970a,  Zaretsky  et  al.  1979). 

Typically,  cracks  begin  to  form  after  a  small 
amount  of  strain  has  occurred.  The  acoustic  emis¬ 
sion  results  given  later  indicate  the  strain  level  for 
the  onset  of  visible  cracking  is  4.7  x  10'*  on  aver¬ 
age.  Interestingly,  this  strain  level  agrees  well  with 
Gold’s  (1970a)  observations  on  columnar-grained 
ice  at  -9.5  °C.  He  found  this  strain  level  to  be  rela¬ 
tively  independent  of  stress  provided  it  was  suffi¬ 
cient  to  cause  cracking. 

The  results  show  that  the  manner  in  which  cracks 
accumulate  with  strain  depends  upon  the  grain 
size  (refer  again  to  Fig.  13).  For  the  small-grained 
material,  most  all  the  cracking  occurs  in  the  first 
10"  strain.  Additional  straining  results  in  a  negli¬ 
gible  increase  in  the  number  of  cracks.  However, 
at  the  intermediate  grain  sizes  (approximately  3 
mm),  the  cracking  continues,  but  at  a  much  reduced 
rate  as  straining  proceeds  beyond  10".  Finally,  the 
largest-grained  material  exhibits  a  very  high  initial 
rate  of  cracking  at  strains  below  10"  and  then  con¬ 
tinues  to  generate  cracks  at  a  significant  rate.  At 
total  strains  of  less  than  3  x  10",  these  specimens 
are  so  completely  saturated  with  cracks  that  they 
appear  opaque.  The  crack  density  can  be  esti¬ 
mated  only  from  thin  sections  for  these  specimens. 

These  results,  brought  about  only  by  an  increase 
in  grain  size,  are  in  good  agreement  with  the 
trends  observed  by  St.  Lawrence  and  Cole  (1982). 
These  resulted  from  an  increase  in  applied  stress, 
while  grain  size  remained  constant  at  1 .2  mm  (esti¬ 
mated  by  the  intercept  method)  and  the  test  tem¬ 
perature  was  -5°C.  In  that  work,  an  increase  in 
stress  brought  about  an  increase  in  cracking  activ¬ 
ity  as  indicated  by  acoustic  emissions  monitoring. 


A  brief  comparison  of  the  influence  of  stress  and 
of  grain  size  on  cracking  shows  that  the  increase  in 
grain  size  in  the  present  work  has  an  effect  on  the 
cracking  activity  that  is  very  similar  to  the  effect 
of  an  increase  in  axial  stress.  This  is  not  surpris¬ 
ing,  however,  since  it  is  well  recognized  that  an  in¬ 
crease  in  either  stress  or  grain  size  generally  re¬ 
duces  ductility. 

Creep  behavior 

Grain  size  effects 

The  character  of  the  creep  behavior  seen  in  Fig¬ 
ures  15a-c  is  similar  to  that  found  in  other  work 
for  the  finer-grained  material  at  similar  stress 
levels  (Mellor  and  Cole  1982,  Jacka  1984). 

The  effect  of  grain  size  on  the  creep  curve  can 
be  seen  by  comparing  specimens  62  and  69  in  Fig¬ 
ure  15a.  An  increase  in  grain  size  from  1.5  to  4.7 
mm  causes  a  drop  in  the  strain  at  the  minimum 
creep  rate  from  10"  to  4.2  x  10".  There  is  a  tend¬ 
ency  for  the  larger-grained  material  to  exhibit 
both  a  faster  drop  in  the  primary  creep  rates  and  a 
faster  increase  in  the  tertiary  rates  than  the  fine¬ 
grained  material. 

Some  of  the  tests  (see  Fig.  15a,  specimens  47,  60 
and  62)  exhibited  a  trend  toward  higher  primary 
creep  rates  with  larger  grain  size.  Duval  and 
LeGac  (1980)  observed  this  trend  in  creep  tests  on 
polycrystalline  ice  at  a  temperature  of  -7°C  and  a 
creep  stress  of  approximately  0.5  MPa.  The  same 
workers  also  noted  that  grain  size  exerted  no  ap¬ 
parent  influence  on  the  “steady  state”  creep  rate 
of  their  test  material.  The  results  of  Duval  and 
LeGac  (1980)  are  at  variance  with  results  reported 
by  Baker  (1978),  who  observed  a  significant  effect 
of  grain  size  on  the  steady-state  creep  rate  of  lab¬ 
oratory-prepared  ice.  Baker  found  the  creep  rates 
exhibited  a  minimum  at  a  grain  size  of  1.0  mm  for 
tests  performed  at  temperatures  of  -7  to  -10°C 
and  at  a  creep  stress  of  approximately  0.56  MPa. 
He  attributed  the  observed  reversal  of  the  influ¬ 
ence  of  grain  size  (from  strengthening  to  weaken¬ 
ing  the  material)  to  a  change  in  the  main  deforma¬ 
tion  mechanisms.  He  reasoned  that  the  grain 
boundary  weakening  resulted  from  diffusional 
processes  operative  for  the  small-grained  material 
and  that  the  strengthening  resulted  from  the  oper¬ 
ation  of  the  dislocation-controlled  creep  mecha¬ 
nism. 

Unpublished  work  referenced  by  Jacka  and 
Maccagnan  (1984)  indicates  no  significant  grain 
size  effect  on  the  minimum  creep  rate  of  lab¬ 
oratory-prepared  ice  over  the  grain  size  range  of 
0.8  to  3.4  mm,  at  temperatures  of  -7  and  -10°C 


I 


B 


40 


and  under  creep  stresses  of  0.3  and  0.26  MPa  octa¬ 
hedral  (0.64  and  0.55  MPa  normal).  These  experi¬ 
mental  conditions  cover  the  range  of  Baker’s 
(1978)  tests,  but  the  grain  size  effect  observed  by 
Baker  is  absent.  Thus,  the  work  by  Baker  (1978) 
remains  unsubstantiated.  The  reason  for  the  dis¬ 
agreement  on  grain  size  effects,  however,  is  not 
clear.  Historically,  a  main  difficulty  in  the  field  of 
ice  mechanics  lies  in  the  effect  of  the  specimen 
preparation  procedure  on  the  mechanical  proper¬ 
ties  of  the  material.  Since  there  is  no  standard 
method  for  specimen  preparation,  workers  gener¬ 
ally  begin  with  a  commonly  used  approach  such  as 
packing  a  mold  with  sieved  ice  grains,  evacuating 
and  flooding  the  mold  with  degassed  water  and 
then  freezing  the  resulting  ice-water  mixture. 
However,  details  of  the  procedure,  such  as  the 
source  of  the  seed  grains,  the  size  range  of  the  seed 
grains,  the  rate  and  direction  of  freezing  final 
specimen  porosity,  and  the  chemical  purity  of  the 
melt,  often  go  unreported.  These  factors  can  in¬ 
fluence  the  mechanical  behavior  of  the  material 
under  certain  conditions,  and  when  data  from  dif¬ 
ferent  sources  are  compared,  possible  specimen 
differences  must  always  be  considered.  In  addi¬ 
tion,  when  grain  size  is  varied,  questions  regarding 
the  influence  of  specimen  size  generally  arise  as 
well.  For  example,  Baker’s  (1978)  specimens  were 
19.7  mm  in  diameter  and  his  grain  diameter  ranged 
from  0.62  to  2.11  mm.  Duval  and  LeGac  (1980) 
used  specimens  of  80-mm  diameter  and  their  grain 
size  range  was  1.07  to  9.8  mm.  Thus,  although 
stress  and  temperature  were  the  same  for  both  sets 
of  data,  the  sample  sizes,  and  hence  the  number  of 
grains  across  a  sample  diameter  for  a  given  grain 
size,  vary  greatly. 

Unfortunately,  the  works  cited  above  are  not 
strictly  germane  to  the  present  study  because  of 
the  significant  difference  in  creep  stress  levels.  The 
higher  stress  level  generally  results  in  material  be¬ 
havior  in  the  dislocation  glide  with  cracking  re¬ 
gime  rather  than  a  diffusion  controlled  regime. 
Also,  the  grain  size  range  of  the  present  work  in¬ 
duces  a  significant  change  in  the  material’s  re¬ 
sponse  to  stress  by  causing  the  onset  of  internal 
fracturing.  Thus  the  grain  size  effect  found  here  is 
only  relevant  when  considering  the  onset  of  inter¬ 
nal  cracking.  A  study  of  grain  size  effects  near  the 
ductile-to-brittle  transition  offers  an  inherent  ad¬ 
vantage  since  the  effect  of  the  grain  size  variations 
is  evidenced  by  visible  cracking.  Thus,  a  grain  size 
effect,  and  the  associated  shift  in  deformational 
mechanism,  can  be  verified  visually.  This  is  a  pref¬ 
erable  situation  to  the  case  cited  above,  where 
stress-strain  rate  data  were  the  only  evidence  of  an 


apparent  deformational  mechanism  change,  and 
no  independent  means  of  verification  was  avail¬ 
able. 

In  Figure  16,  which  shows  minimum  creep  rate 
vs  the  average  grain  size,  there  appears  to  be  a 
subtle  trend  for  the  lowest  values  of  minimum 
creep  rate  to  occur  near  a  grain  size  of  3.0  mm. 
The  creep  rates  at  the  largest  grain  sizes  exhibit  a 
fairly  large  degree  of  scatter,  however,  making  it 
difficult  to  discern  a  trend  beyond  the  3-mm  grain 
size. 

It  is  interesting  to  note  that  the  more  clearly  de¬ 
fined  drop  in  f„,„  for  grain  sizes  between  1 .5  and  3 
mm  coincides  with  the  transition  from  the  thresh¬ 
old  of  cracking  to  a  significant  degree  of  cracking. 
Over  this  same  range  in  grain  size,  the  strain  at  f„,„ 
undergoes  a  significant  drop  from  10'2  to  approxi¬ 
mately  5.5xlO*3.  Thus,  the  material  appears  to 
lose  ductility  as  a  result  of  the  grain  size  increase. 
A  good  deal  more  testing  will  be  needed  to  clarify 
the  trends  in  these  creep  results. 

It  is  possible  that  the  behavior  seen  in  Figure  16 
is  merely  the  result  of  random  variations  in  the 
balance  between  competing  deformational  mecha¬ 
nisms.  This  is  an  inherent  problem  at  the  transi¬ 
tion  point  between  two  distinct  regimes  of  materi¬ 
al  behavior. 

Another  possibility  for  the  apparent  grain  size 
effect  for  the  larger  grain  sizes  relates  to  specimen 
size  effects.  When  grain  size  varies  as  in  the  pres¬ 
ent  work,  the  number  of  grains  in  a  specimen  of 
fixed  dimensions  varies  greatly,  as  does  the  num¬ 
ber  of  grains  across  the  diameter.  In  fact,  a  few  of 
the  larger-grained  specimens  tested  are  somewhat 
over  the  acceptable  limit  of  10  to  12  grains  across 
the  diameter.  (Note,  however,  that  when  using  the 
results  of  the  intercept  method  of  grain  size  esti¬ 
mation,  all  specimens  appear  to  be  within  the  limit 
of  10  grains  across  the  diameter.)  Jones  and  Chew 
(1983)  recommended  having  at  least  12  grains 
across  the  diameter  to  avoid  specimen  size  effects. 
Their  results  indicated  a  noticeable  increase  in  uni¬ 
axial  compressive  strength  when  the  number  of 
grains  across  the  specimen  dropped  to  eight.  In 
these  tests,  grain  size  was  held  constant  at  1 .0  mm 
and  the  specimen  size  was  changed  to  achieve  the 
range  in  the  number  of  grains  per  diameter.  There 
is  still  some  uncertainty  as  to  specimen  size  effects 
in  the  testing  of  ice  and  it  is  possible  that  the  pres¬ 
ent  testing  methods  do  not  completely  isolate 
grain  size  effects  from  possible  specimen  size  ef¬ 
fects.  A  considerable  amount  of  work  will  be 
needed,  however,  to  clarify  the  roles  of  grain  size 
and  specimen  size  in  the  mechanical  testing  of  ice. 


41 


Potential  difficulties  in  this  regard  are  recog¬ 
nized,  but  since  it  is  not  of  primary  concern  in  the 
present  work,  this  matter  will  not  be  dealt  with 
further. 

The  effect  of  grain  growth 

An  interesting  aspect  of  material  behavior  came 
to  light  regarding  the  effect  of  time/temperature 
history  on  the  creep  response  of  the  ice.  Specimen 
grain  size  is  generally  controlled  by  the  seed  grain 
size  and  a  given  sample  is  tested  soon  after  mold¬ 
ing  to  avoid  grain  growth  effects.  However,  a 
large  average  grain  size  can  be  achieved  by  suit¬ 
ably  aging  a  smaller  grain-sized  specimen.  The 
question  naturally  arises  as  to  whether  specimens 
of  equal  grain  size  display  similar  mechanical  be¬ 
havior  regardless  of  the  method  used  to  achieve 
the  grain  size.  Figure  15f  shows  data  which  ad¬ 
dress  this  point.  The  grain  sizes  of  specimens  41, 
49  and  56  in  Figure  1 5 f  were  achieved  by  allowing 
grain  growth  to  occur  for  some  time  after  mold¬ 
ing.  The  seed  grains  for  these  specimens  were  in 
the  0.59-0.83  mm  range.  The  grain  size  in  all  other 
tests  resulted  directly  from  the  seed  grain  size  and 
no  significant  grain  growth  occurred  before 
testing.  The  difference  in  the  creep  behavior  bet¬ 
ween  the  two  groups  of  specimens  is  striking. 
Specimens  41  and  49  do  not  exhibit  minimum 
strain  rates  as  such,  and  56  merely  develops  a  sub¬ 
tle  trend  near  10'!  strain  somewhat  indicative  of  a 
minimum  strain  rate.  The  common  trend  here  is 
the  absence  of  the  decreasing  strain  rate  usually 
found  in  primary  creep.  Additionally,  these 
specimens  always  show  an  extreme  degree  of  inter¬ 
nal  cracking. 

The  reasons  for  the  anomalous  behavior  of  the 
grain-growth  specimens  are  unclear.  It  is  unlikely 
that  a  preferred  orientation  developed  during 
grain  growth  under  these  conditions  when  the 
grains  were  originally  randomly  oriented.*  A  pos¬ 
sible  explanation  may  be  related  to  the  dislocation 
density  of  the  material  just  prior  to  testing.  The 
grain-growth  specimens,  after  being  aged  for  sev¬ 
eral  weeks  at  a  relatively  warm  temperature  (i.e. 
-2°C),  presumably  had  a  significantly  lower  dislo¬ 
cation  density  than  the  specimens  that  were  tested 
shortly  after  molding.  This  difference  in  disloca¬ 
tion  density  can  cause  a  corresponding  difference 
in  the  value  of  the  stress  needed  to  start  disloca¬ 
tion  motion  in  the  two  types  of  specimens.  Arm¬ 
strong  et  al.  (1962)  showed  that  the  frictional 
stress  term  an  increases  as  a  material  undergoes  the 
increase  in  dislocation  density  associated  with 
work  hardening.  If  this  is  the  case,  the  grain- 


Figure  27.  Creep  curve  for  a  fine-grained  specimen 
under  high  load  (a  =  4. 12  MPa). 


grov  th  specimens  will  experience  higher  effective 
shear  stresses  than  the  other  specimens.  This  in 
turn  leads  to  higher  internal  stress  concentrations 
and  hence  the  greater  degree  of  cracking.  Appar¬ 
ently,  this  greater  degree  of  damage  through 
cracking  is  associated  with  a  reduction  in  the 
strain  at  the  minimum  creep  rate  or,  in  some  cases, 
the  absence  of  a  discernible  minimum  creep  rate. 
It  is  expected  that  this  behavior  would  result  if  the 
applied  stress,  in  a  test  on  material  having  a  great¬ 
er  initial  dislocation  density,  was  sufficiently  high 
to  give  the  same  level  of  effective  shear  stress. 
Some  evidence  exists  in  support  of  this,  namely 
fine-grained  ice  without  any  grain  growth  was 
found  to  experience  only  a  brief  strain  rate  mini¬ 
mum  at  3.4  xlO'3  strain  under  a  stress  of  4.12 
MPa  (see  Fig.  27).  A  severe  amount  of  cracking 
accompanied  this  behavior.  Specimens  subjected 
to  slightly  lower  stresses,  however  (i.e.  3.7  MPa), 
exhibit  typical  creep  behavior  (see,  for  example, 
Mellor  and  Cole  1982)  and  strains  at  tm,„  are  near 
10  !.  Presumably,  the  strain  rate  minimum  would 
disappear  completely  under  some  further  increase 
in  stress.  Thus,  there  is  an  indication  that,  at  some 
level  of  effective  shear  stress,  ice  essentially  fails 
upon  loading  and  does  not  develop  the  strain  rate 
trends  typical  of  creep  behavior. 

An  additional  factor  complicating  an  assess¬ 
ment  of  the  observed  behavior  is  that  the  speci¬ 
mens  experiencing  grain  growth  are  likely  to  have 
a  rather  broad  range  in  grain  sizes  because  the 
larger  grains  grow  at  the  expense  of  the  smaller 


A.J.  <»ow,  pers.  comm.  198.1. 


42 


% 


a.  Thin  section  of  an  untested 
specimen  showing  an  extreme  ex¬ 
ample  of  the  grain  growth  pro¬ 
cess. 


b.  Thin  section  of  specimen  49 
after  testing.  Note  the  range  in 
grain  size  resulting  from  the  grain 
growth  process. 


Figure  28.  The  effect  of  grain  growth  on  grain  size. 


grains.  Figure  28a  shows  an  extreme  example  of 
this.  It  shows  an  untested  specimen  held  at  -2°C 
for  approximately  three  months  before  the  section 
was  taken.  It  exhibits  abnormal  grain  growth  as 
well  as  an  extremely  broad  range  in  apparent  grain 
diameters.  Figure  28b  shows  a  thin  section  of  spec¬ 
imen  49  after  testing  under  2.8  MPa  to  a  strain  of 
2.5  x  10~\  Note  that  some  grains  have  grown  con¬ 
siderably  while  clusters  of  fine  grains  (near  the 
center  of  the  photograph),  apparently  from  the 
original  structure,  still  persist.  It  is  difficult  to  de¬ 
termine  which  characteristics  of  such  a  structure 
control  the  deformational  processes. 

Due  to  the  uncertainties  involved  and  the  limit¬ 
ed  amount  of  data  available,  it  was  decided  not  to 
pursue  the  effect  of  grain  growth  on  mechanical 
behavior  in  the  present  work.  Once  the  above- 
mentioned  deviations  were  encountered,  speci¬ 
mens  were  tested  only  as  molded,  not  allowing  sig¬ 
nificant  grain  growth  to  occur. 

Normalized  crack  length 

It  is  useful  to  normalize  the  crack  length  data 
given  in  Appendix  A  to  the  grain  size  of  each  spec¬ 
imen.  This  allows  a  broad  comparison  of  the  re¬ 
sults  and  sheds  light  on  the  relationship  between 
the  crack  size  distribution  and  the  grain  size.  Fig¬ 
ure  29  shows  a  histogram  of  some  2246  observa¬ 
tions  made  from  the  thick  sections.  These  data 
have  been  normalized  to  grain  size.  The  mean  is 
0.5  and  the  standard  deviation  is  0.39.  Table  4 
gives  the  values  of  the  normalized  mean  crack 


length  for  all  specimens  (CL/d).  Although  these 
values  display  a  certain  amount  of  scatter,  they  are 
reasonably  well  grouped  about  the  mean.  Interest¬ 
ingly,  the  distribution  of  the  merged  normalized 
data  retains  essentially  the  same  shape  as  the  raw 
crack  size  data  of  the  individual  specimens  in  Ap¬ 
pendix  A.  Given  the  above  observations,  it  ap¬ 
pears  likely  that  a  generalized  distribution,  such  as 
that  in  Figure  29,  in  terms  of  normalized  crack 
length,  may  be  used  to  estimate  the  actual  crack 
size  distribution  for  any  given  grain  size. 

The  main  difficulty  in  this  connection  lies  in  as¬ 
sessing  the  maximum  crack  length.  There  is  con¬ 
siderable  scatter  in  the  largest  normalized  crack 
length  values  for  the  specimens  tested.  Figure  30 
shows  the  maximum  normalized  crack  length  as  a 
function  of  grain  size  for  all  tests.  They  range 
from  0.83  to  3.10  and  do  not  appear  to  correlate 
with  either  grain  size  or  axial  strain  level.  Perhaps 
fortuitously,  the  maximum  crack  size  of  3Ad 
agrees  with  the  observations  made  by  McMahon 
and  Cohen  (1965)  cited  earlier.  The  average  of  the 
maximum  normalized  crack  lengths  is  1.70  with  a 
standard  deviation  of  0.66.  Additionally,  the  raw 
data  indicate  that  8.8%  of  the  observed  cracks  are 
greater  in  length  than  the  average  grain  size. 

A  Beta-distribution  fit  to  all  the  data  indicates 
that  the  probability  of  encountering  a  crack  equal 
to  or  larger  than  1 .6 d  is  1  %  and  the  probability  of 
encountering  a  crack  equal  to  or  larger  than  2.0 d 
is  0.!°7o,  In  other  words,  it  is  relatively  rare  to  en¬ 
counter  a  crack  larger  than  the  average  maximum 


Normolii»d  Frocture  Length 


Figure  29.  Normalized  fracture  length  distribution  for  alt 
tests. 


MeonGrom  Oiameter  (mm) 


Figure  30.  Maximum  normalized  crack 
length  vs  grain  diameter  for  all  tests. 


value.  In  fact,  all  observed  cracks  with  normalized 
values  greater  than  2.2  occurred  in  either  specimen 
71  or  74.  The  reason  for  the  unusually  high  values 
in  these  particular  specimens  is  not  apparent,  but 
the  likelihood  of  their  existence  must  nonetheless 
be  considered  in  applying  these  results. 

An  estimate  of  the  actual  crack  size  distribution 
of  material  with  an  arbitrary  grain  size  d  can  be 
obtained  from  the  normalized  crack  size  distribu¬ 
tion  by  substituting  the  term  CL/d  for  the  normal¬ 
ized  crack  size  CLN  and  then  multiplying  the  coef¬ 
ficient  by  l/d  to  maintain  unit  area  of  the  proba¬ 
bility  density  function. 

Location  of  cracks 

As  mentioned  above  (see  Table  3),  thin  sections 
of  several  highly  cracked  specimens  were  examined 
in  detail  in  order  to  assess  the  location  of  the  mi¬ 
crofractures.  The  microfractures  were  categorized 
as  either  grain  boundary  or  transcrystalline.  In 
total,  573  observations  were  made  and  Figure  31 


shows  the  results  in  the  form  of  histograms.  These 
data  have  been  normalized  to  grain  size. 

All  of  these  specimens  were  strained  to  10~J 
under  the  2.0-MPa  initial  creep  stress.  There  is  no 
apparent  systematic  variation  of  crack  location 
with  grain  size  under  these  conditions. 

The  mean  lengths  of  the  normalized  grain  boun¬ 
dary  and  transcrystalline  cracks  were  0.37  and 
0.35  respectively.  The  maximum  values  were  1.6 
and  1.2  respectively.  The  fact  that  these  measure¬ 
ments  came  from  thin  sections  probably  led  to  the 
lower  mean  and  extreme  values  relative  to  results 
obtained  from  thick  sections.  It  would  be  highly 
unlikely  for  the  maximum  crack  dimension  to  lie 
in  an  arbitrarily  selected  thin  section  of  1  mm, 
while  the  probability  of  observing  the  complete 
length  of  a  crack  in  a  thick  section  (of  10  mm)  is 
much  greater.  Thus,  the  absolute  magnitude  of  the 
results  in  Figure  31  should  be  treated  with  some 
caution. 


0  04  0  8  12  16 


Normolized  Crack  Length 

a.  Normalized  grain  boundary  crack  size  distribution. 


0  0.4  0  8  12 

Normalized  Crack  Length 


b.  Normalized  transcrystalline  crack  size 
distribution. 

Figure  31.  Normalized  crack  length  histograms. 


Acoustic  emission  activity 

In  the  present  work,  the  acoustic  emission  data 
serve  as  a  vehicle  to  link  the  fracturing  activity 
with  time  and  thus  specimen  strain.  The  initial 
task  concerns  the  development  of  a  correspond¬ 
ence  between  an  acoustic  event  and  the  nucleation 
of  a  discernible  microfracture.  The  correspond¬ 
ence  is  based  on  the  reasonable  assumption  that 
the  recorded  AE  event  amplitude  is  in  proportion 
to  the  microfracture  size,  as  noted  in  an  earlier 
section. 

The  crack  density  measurements  allow  the  esti¬ 
mation  of  the  total  number  of  visible  cracks  in  a 
given  specimen.  The  AE  monitoring  system  is  set 


to  a  sensitivity  great  enough  to  respond  to  acoustic 
activity  of  much  lower  amplitudes  than  that  gener¬ 
ated  by  the  observable  microfractures.  Thus,  in  a 
given  test,  there  are  generally  many  more  AE 
events  recorded  than  cracks  nucleated.  Conse¬ 
quently,  filtering  the  AE  data  was  necessary  in 
such  a  manner  as  to  retain  the  appropriate  number 
of  events  corresponding  to  the  estimated  total 
number  of  microfractures  in  the  specimen.  Events 
were  filtered  with  respect  to  amplitude  only.  A 
computer  program  performed  the  filtering  process 
in  two  modes:  1)  given  a  threshold  amplitude 
level,  it  determined  the  number  of  events  having 
amplitudes  greater  than  or  equal  to  the  threshold 


45 


using  a  simple  sorting  method,  and  2)  given  a  spe¬ 
cific  number  of  events,  it  determined  the  AE  am¬ 
plitude  threshold  that  was  passed  the  required 
number  of  times.  The  latter  mode  proved  most 
useful  in  the  present  context.  The  program  was  en¬ 
tered  with  the  estimated  number  of  microfractures 
and  an  output  file  was  in  turn  generated  that  con¬ 
tained  only  the  AE  events  that  passed  the  filtering 
process.  The  file  contained  the  time  of  occurrence 
and  the  amplitude  of  each  event. 

In  most  tests,  a  remotely  controlled  solenoid  im¬ 
parted  a  trigger  signal  to  the  specimen  at  the  mo¬ 
ment  the  load  application  began.  The  AE  system 
sensed  this  signal  and  its  time  of  occurrence  was 
taken  as  the  zero  or  reference  time  for  the  test. 
The  deformation  readings  also  were  “zeroed”  to 
this  time  to  ensure  a  common  starting  time  for 
both  the  AE  and  deformation  data.  Due  to  the 
method  of  recording  test  information,  two  sepa¬ 
rate  files  were  initially  developed  for  each  test. 
One  consisted  of  AE  data  as  a  function  of  time 
and  another  was  deformation  as  a  function  of 
time.  Both  files  were  interpolated  to  yield  readings 
at  the  same  time  increments  and  merged  to  form  a 
single  file. 

The  resulting  file  contained  sufficient  informa¬ 
tion  to  determine,  for  specific  time  increments,  the 
specimen  strain,  strain  rate,  stress,  accumulated 
fractures,  fracturing  activity  per  unit  time  and  per 
unit  strain.  The  acoustic  activity  was  normalized 
to  unit  volume  in  these  calculations. 

An  eventual  goal  of  the  AE  work  is  to  firmly  es¬ 
tablish  a  correspondence  between  acoustic  activity 
and  fracturing  activity.  This  relationship  will  al¬ 
low  a  prediction  of  the  size  distribution  of  the 
fractures  generating  the  observed  acoustic  activi¬ 
ty.  However,  at  this  writing,  this  relationship  is 
not  yet  sufficiently  established  to  warrant  a  de¬ 
tailed  analysis.  For  the  present  the  filtered  AE  re¬ 
sults  may  be  reasonably  taken  to  indicate  the  oc¬ 
currence  of  visible  cracks.  The  AE  observations 
for  each  test  are  based  on  filtered  data  employing 
the  filtering  thresholds  determined  for  each  speci¬ 
men. 

The  results  allow  the  determination  of  the  time 
and  strain  at  the  onset  of  fracturing  as  well  as  at 
the  peak  fracturing  rate,  as  given  in  an  earlier  sec¬ 
tion. 

With  the  exception  of  specimens  43,  49,  55  and 
70,  the  amplitude  thresholds  fall  within  the  range 
of  81 .6  to  88.7  dB,  with  a  mean  and  standard  devi¬ 
ation  of  86.2  dB  and  2.0  dB.  When  all  data  are 
considered,  the  mean  amplitude  threshold  is  83.7 
dB  with  a  standard  deviation  of  4.7  dB.  It  is  not 


clear  why  the  four  specimens  mentioned  have  sig¬ 
nificantly  lower  filtering  thresholds,  but  there  are 
several  sources  of  error  that  could  contribute  to 
inaccuracies  in  the  AE  measurements: 

1)  inconsistencies  in  the  characteristics  of  the 
specimen-transducer  interface 

2)  signal  attenuation 

3)  crack  orientation  effects 

4)  frequency  effects. 

A  variable  in  the  AE  considerations  for  all  tests 
is  the  consistency  or  repeatability  of  the  character¬ 
istics  of  the  specimen-transducer  interface.  Al¬ 
though  a  great  effort  was  made  to  be  as  consistent 
as  possible  in  the  placement  of  the  transducers, 
variations  in  the  quality  of  the  specimen/trans¬ 
ducer  interface  can  nonetheless  occur.  The  meas¬ 
ured  amplitude  of  identical  acoustic  pulses  de¬ 
creases  with  poor  specimen-transducer  contact. 
Ideally,  the  system  should  be  calibrated  with  an 
acoustic  pulse,  similar  to  that  generated  by  a 
nucleating  crack,  just  prior  to  each  test.  Thus,  de¬ 
ficiencies  could  be  detected  beforehand  and  the 
transducer  remounted  to  provide  a  satisfactory  re¬ 
sult.  Unfortunately,  such  a  method  was  not  avail¬ 
able  during  the  course  of  this  study,  so  some  un¬ 
certainty  is  inherent  in  the  AE  results. 

In  fact,  such  uncertainty  could  be  the  major 
cause  of  variations  in  the  filtering  thresholds  (see 
Table  5).  This  circumstance  causes  difficulty  in  the 
longer-range  objective  of  establishing  an  overall 
amplitude  threshold  for  visible  fractures.  How¬ 
ever,  it  does  not  adversely  affect  the  veracity  of 
the  results  when  specimens  are  considered  individ¬ 
ually.  Thus,  even  though  the  thresholds  may  vary, 
the  filtered  AE  events  for  a  particular  specimen 
correspond  to  the  observed  number  of  cracks  for 
that  specimen.  Consequently,  such  quantities  as 
the  cracking  rate  and  the  strain  level  for  the  onset 
or  peak  rate  of  cracking  are  not  directly  influenced 
by  small  variations  in  the  specimen-transducer  in¬ 
terface  quality. 

Attenuation  of  the  acoustic  signal  is  significant 
for  high  frequencies  and  large  distances  in  ice. 
However,  in  this  study,  the  maximum  travel  dis¬ 
tance  from  an  event  source  to  one  of  the  trans¬ 
ducers  is  approximately  50  mm.  Bogorodskii  and 
Gusev  (1973)  indicate  that  attenuation  is  on  the 
order  of  5  dB  m'1  in  ice.  Thus,  signal  variations  of 
much  less  than  1  dB  are  expected  in  the  present 
work,  and  are  thus  not  a  significant  factor  in  the 
results. 

The  orientation  of  the  crack  to  the  transducer 
face  is  likely  to  have  an  effect  on  the  measured 
amplitude.  The  effect  is,  however,  difficult  to 


46 


.i75  r 

44 Ve  -  .  - 


£  801 — 
<  .69 


o  (- 


2  3 

Meon  Crock  Length  (mm) 


Figure  32.  Mean  AF  amplitude  vs  mean  crack  length. 


quantify.  It  is  assumed  that  the  orientation  of  the 
cracks  to  the  transducer  face  is  sufficiently  ran¬ 
dom  to  preclude  systematic  effects  of  this  varia¬ 
ble. 

This  treatment  does  not  address  the  effects  of 
possible  variations  in  the  frequency  content  of  the 
acoustic  pulses.  Since  the  mechanics  of  crack  for¬ 
mation  are  expected  to  be  the  same  for  all  crack 
sizes,  little  variation  is  expected.  However,  the 
possibility  that  the  frequency  spectra  of  the  acous¬ 
tic  pulses  may  change  with  crack  size  should  be 
kept  in  mind. 

As  pointed  out  in  an  earlier  section,  a  micro- 
fracture  is  expected  to  generate  an  acoustic  pulse 
in  proportion  to  its  size,  with  certain  geometric 
considerations.  Thus,  the  magnitude  of  the  acous¬ 
tic  pulses  passing  the  filter  should  correspond  to 
the  sizes  of  the  observed  microfractures.  Figure  32 
shows  the  average  AE  amplitude  vs  the  average 
crack  size  for  all  the  specimens  for  which  suitable 
AE  data  were  obtained.  Included  in  this  plot  is  a 
point  from  specimen  69,  which  evidenced  no  visi¬ 
ble  cracking.  This  amplitude  of  79  dB  was  very 
rarely  exceeded  in  the  test  and  is  assumed  to  repre¬ 
sent  the  greatest  AE  amplitude  produced  by  a  sub- 
visible  crack. 

These  data  indicate  the  tendency  for  the  mean 
AE  amplitude  to  increase  with  mean  crack  size. 
The  scatter,  however,  is  considerable  and,  as  men¬ 
tioned  above,  this  scatter  is  probably  due  to  varia¬ 
tions  in  the  quality  of  the  specimen/transducer  in¬ 
terface.  The  average  crack  size  -  average  ampli¬ 
tude  relationship  could  be  strengthened  by  an  in¬ 
crease  in  the  relatively  narrow  range  of  0.90  to  2.5 
mm  in  the  average  crack  size.  Significantly  larger 
specimens  would  be  required  to  increase  this  range. 

The  onset  of  cracking,  as  indicated  by  the  AE 
results,  occurs  at  an  axial  strain  of  4.7  x  10  4  with  a 
standard  deviation  of  4.3  x  10'4.  Interestingly,  this 


strain  level  is  in  good  agreement  with  that  given  by 
Gold  (1967)  for  the  strain  at  the  formation  of 
grain-sized  cracks  in  columnar-grained  ice.  The 
strain  and  time  at  the  onset  of  cracking  activity  do 
not  appear  to  vary  systematically  with  grain  size  in 
these  tests.  Strain  values  for  the  cracking  onset 
range  from  effectively  zero  to  a  maximum  of 
1.15x10'. 

As  Figure  23  shows,  grain  size  exerts  a  strong  in¬ 
fluence  on  the  time  to  the  maximum  cracking  rate 
(as  indicated  by  the  maximum  AE  rate).  Since  the 
strain  at  \dAE/dt\„,„  is  not  strongly  affected  by 
the  grain  size  in  these  tests,  it  is  evident  that  the 
average  strain  rate  prior  to  the  peak  cracking  rate 
must  increase  with  grain  size.  Indeed,  an  inspec¬ 
tion  of  the  creep  curves  (Fig.  15c)  shows,  for  a 
constant  initial  stress  of  2.0  MPa,  that  the  average 
strain  rate  prior  to  [dAE/di]„ax  increases  by  nearly 
a  factor  of  four  as  grain  size  increases  from  1 .8  to 
5.5  mm.  There  is  a  very  moderate  tendency  for  the 
strain  at  \dAE/dt]mxx  to  decrease  with  increasing 
grain  size,  further  contributing  to  observed  de¬ 
crease  in  time  to  the  maximum  cracking  rate.  The 
average  strain  at  [dAE/de]ma.  is  1.95x10'’  with  a 
standard  deviation  of  9.6  xlO  4.  The  average 
strain  at  [ dAE/dt\ma ,  is  1 .75  x  10'’  with  a  standard 
deviation  of  8.8  x  10\ 

In  general,  these  results  reinforce  earlier  find¬ 
ings  regarding  cracking  in  polycrystalline  ice.  A 
small  amount  of  strain  is  required  to  initiate 
cracking,  and  once  started,  the  rate  of  cracking 
reaches  a  peak  during  the  primary  creep  stage, 
well  before  the  minimum  creep  rate  is  reached. 

The  average  strain  at  which  [dAE/dt]m.x  occurs 
coincides  with  the  average  strain  at  the  in¬ 
flection  point  found  in  the  primary  creep  portion 
of  a  plot  of  e  vs  f  (see  Fig.  15).  (Both  these  values 
of  average  strain  are  very  near  2x10"’.)  In  the 
present  deformational  mechanism  regime  of  plas- 


z  >»  > 


tic  flow  with  cracking,  AE  results  generally  show 
no  distinct  characteristic  at  either  the  occurrence 
of  in  a  creep  test  or  in  a  strength  test  (see 
Cole  and  St.  Lawrence  1984).  However,  it  is  ex¬ 
pected  that  the  maximum  cracking  rate  should 
coincide  with  a  fundamentally  significant  aspect 
of  material  behavior.  Mellor  and  Cole  (1982)  were 
the  first  to  distinguish  the  point  of  in  ice  creep 
data,  and  noted  that  it  is  the  point  of  maxi¬ 
mum  deceleration  in  the  primary  creep  curve. 
Thus,  the  AE  results  indicate  that  the  material  is 
apparently  undergoing  its  greatest  rate  of  strain 
hardening  (i.e.  creep  rate  is  decreasing  most  rapid¬ 
ly)- 

Although  this  application  of  AE  technology  re¬ 
quires  further  development,  the  potential  for  its 
use  is  clear.  Proper  interpretation  of  AE  data  will 
preclude  the  time-consuming  post-test  analysis 
currently  required  for  examining  internal  cracking 
activity.  Much  insight  can  be  gained  from  detailed 
information  on  the  characteristics  of  internal  frac¬ 
tures  in  ice  in  terms  of  understanding  deformation 
mechanisms  and  for  verification  of  micromechan¬ 
ical  models  of  material  behavior. 


SUMMARY  AND  CONCLUSIONS 

This  work  presents  the  results  of  constant  load 
creep  tests  performed  at  -5°C  on  polycrystalline 
ice.  Some  26  tests  were  performed  on  specimens 
having  equiaxed  grains  ranging  from  1.5  to  6.0 
mm.  Most  specimens  experienced  an  initial  stress 
of  2.0  MPa.  Tests  were  terminated  after  axial 
strains  ranging  from  3.7x10  4  to  5x10*.  Some 
specimens  were  tested  at  higher  stress  levels  of  2.4, 
2.6  and  2.8  MPa. 

The  results  demonstrate  the  influence  of  grain 
size  on  the  internal  fracturing  in  ice.  The  stated  in¬ 
crease  in  grain  size  brought  about  the  onset  of  in¬ 
ternal  cracking  as  predicted  by  the  nucleation 
equation  of  Smith  and  Barnby  (1967).  The  materi¬ 
al  showed  a  loss  in  ductility  as  evidenced  by  a  sig¬ 
nificant  decrease  in  the  strain  at  and  a  dram¬ 
atic  increase  in  the  number  of  internal  cracks. 

In  all  tests  where  internal  cracking  occurred,  an 
extensive  post-test  analysis  on  the  size  and  number 
of  cracks  in  the  ice  was  made.  This  analysis  al¬ 
lowed  the  determination  of  the  crack  size  distribu¬ 
tion  as  well  as  the  crack  density  in  each  specimen. 
A  linear  relationship  between  grain  size  and  the 
average  crack  size  distribution  emerged  from  these 
data. 

Peripheral  aspects  of  the  work  addressed  crack 
healing,  the  theoretical  aspects  of  the  grain  size/ 


crack  size  relationship,  the  grain  size  effect  on  the 
strain  at  <«,„  the  relationship  between  grain  size 
and  slip  plane  length  and  the  effect  of  grain  size  on 
creep  behavior. 

Acoustic  emissions  monitoring  techniques  were 
employed  and  the  results  were  promising.  Consid¬ 
erable  progress  was  made  toward  determining  the 
onset,  total  number  and  rate  of  formation  of  mi¬ 
crocracks  from  AE  data. 

In  view  of  the  test  conditions  stated  above,  this 
work  leads  to  the  following  conclusions: 

1.  Both  the  crack  nucleation  condition  and  the 
crack  size/grain  size  relationship  are  well  modeled 
using  the  concept  of  the  dislocation  pileup. 

2.  Cracks  begin  to  nucleate  in  ice  at  grain  sizes 
between  1.5  and  1.8  mm  under  a  2.0-MPa  creep 
stress  at  -5  °C. 

3.  The  extent  of  internal  microfracturing  in¬ 
creases  sharply  as  grain  size  increases  from  1.8  to 
6.0  mm. 

4.  The  average  microcrack  dimension  scales 
linearly  with  the  mean  grain  size. 

5.  As  grain  size  increases  from  1.5  to  6.0  mm, 
the  axial  strain  at  the  minimum  creep  rate  falls 
from  10'!  to  near  4x10"*. 

6.  The  minimum  creep  rate,  while  exhibiting 
some  subtle  trends,  is  not  clearly  affected  by  grain 
size. 

7.  The  peak  fracturing  rate  occurs  at  relatively 
low  strains,  well  before  tm,„  is  reached,  and  the 
time  to  the  peak  fracturing  rate  decreases  with  in¬ 
creasing  grain  size. 

8.  Grain  size  apparently  does  not  systematical¬ 
ly  affect  the  strain  at  the  onset  of  cracking  or  the 
strain  at  the  peak  fracturing  rate. 

9.  Based  on  a  limited  number  of  observations, 
grains  that  develop  transgranular  cracks  do  not 
appear  to  have  a  preferred  orientation  to  the  stress 
axis. 

10.  Crack  healing  processes  significantly  affect 
crack  size.  Water-vapor-filled  cracks  heal  by  a  vis¬ 
cous  flow  mechanism  at  a  significantly  higher  rate 
than  air-filled  cracks. 

11.  The  crack  lengths  for  all  specimens,  when 
normalized  to  grain  size,  tend  to  follow  a  common 
distribution. 


SUGGESTIONS  FOR  FUTURE  WORK 

1.  Experimental  work  must  be  carried  out  to  ex¬ 
plore  specimen  size  effects  on  the  mechanical  be¬ 
havior  of  polycrystalline  ice.  This  should  be  done 
in  conjunction  with  a  grain  size  study  in  order  to 
isolate  grain  size  and  specimen  size  effects. 


'.'  Me1!  *  l«  rf  r 


2.  Both  strength  and  creep  tests  on  specimens  of 
varying  grain  size  should  be  performed  both  above 
and  below  the  threshold  of  cracking  as  indicated 
in  this  work.  This  would  help  clarify  the  trends 
suggested  in  the  present  data.  Specifically,  such  re¬ 
sults  would  show  if  grain  size  exerts  an  influence 
on  the  stress  vs  strain  rate  relationship  to  accom¬ 
pany  its  influence  on  the  internal  fracturing  activi¬ 
ty- 

3.  Continued  efforts  toward  establishing  a  crack 
size  vs  AE  amplitude  relationship  appear  warrant¬ 
ed.  A  useful  relationship  of  this  type  would  greatly 
reduce  the  amount  of  work  required  to  analyze 
fracturing  activity.  The  optical  post-test  analysis 
methods  used  in  this  work  are  too  time-consuming 
and  tedious  to  become  part  of  a  routine  testing 
procedure.  However,  the  AE  technique,  once  suf¬ 
ficiently  advanced,  will  lend  itself  to  routine  use. 

4.  A  detailed  study  of  crack  orientation  to  the 
axis  of  applied  stress,  especially  under  uniaxial 
tension,  would  be  useful.  Given  a  sufficient  num¬ 
ber  of  observations,  it  is  possible  to  establish  a 
distribution  of  the  angles  between  the  crack  plane 
and  the  stress  axis.  Knowledge  of  this  distribution 
as  well  as  its  development  during  the  course  of 
straining  will  shed  light  on  the  failure  process  of 
ice  in  tension. 

5.  Cracking  in  specimens  having  grains  signifi¬ 
cantly  larger  than  those  tested  in  this  work  should 
be  examined.  It  is  possible  that  subgrain  structure 
might  become  a  factor  at  large  grain  sizes  and  thus 
limit  the  applicability  of  the  crack  size  vs  grain  size 
relationships  found  in  the  present  work. 

6.  The  effects  of  grain  growth  on  the  mechani¬ 
cal  properties  of  ice  should  be  examined  system¬ 
atically.  It  is  possible  the  time-temperature  history 
should  be  considered  as  a  test  variable  along  with 
structural  parameters. 


LITERATURE  CITED 

Agarwal,  A.B.L.,  J.R.  Frederick  and  D.K.  Fel- 
beck  (1970)  Detection  of  plastic  microstrain  in 
aluminum  by  acoustic  emission.  Met.  Trans.,  1: 
1069-1071. 

Armstrong,  R.W.  (1970)  The  influence  of  grain 
size  on  several  mechanical  properties  of  material. 
Met.  Trans.,  1:  1169-1176. 

Armstrong,  R.W.,  I.  Gold,  R.M.  Douthwaite  and 
N.J.  Petch  (1962)  The  plastic  deformation  of 
polycrystalline  aggregates.  Philosophical  Maga¬ 
zine,  7:  45-58. 

Baker,  R.W.  (1978)  The  influence  of  ice  crystal  on 
creep.  Journal  of  Glaciology,  21(85):  485-497. 


Baram,  J.  and  M.  Rosen  (1981)  Effect  of  grain 
size  on  the  acoustic  emission  generated  during 
plastic  deformation  of  copper.  Materia!  Science 
and  Engineering,  47:  243-246. 

Bogorodskii,  V.V.  and  A.V.  Gusev  (1973)  Attenu¬ 
ation  of  sound  in  ice  in  the  frequency  range  200- 
1100  kHz.  Sov.  Phys.  Acoust.,  19(2),  Sept-Oct: 
97-99. 

Bullough,  R.  (1964)  The  cracked  dislocation  under 
tension.  Philosophical  Magazine,  8th  series, 
9(102):  917-925. 

Carter,  D.  (1970)  Brittle  fracture  of  snow  ice.  Pro¬ 
ceedings,  IAHR  Ice  Symposium,  Reykjavik,  pp. 
1-8. 

Colbeck,  S.C.  (1980)  Thermodynamics  of  snow 
metamorphism  due  to  variations  in  curvature. 
Journal  of  Glaciology,  26(94):  291-301. 

Colbeck,  S.C.  (1986)  Theory  of  microfracture 
healing  in  ice.  Acta  Met.,  34(7):  89-95. 

Cole,  D.M.  (1979)  Preparation  of  polycrystalline 
ice  specimens  for  laboratory  experiments.  Cold 
Regions  Science  and  Technology,  1(2):  153-159. 
Cole,  D.M.  (1984)  The  amplitude  of  acoustic 
emissions  in  ice.  USA  Cold  Regions  Research  and 
Engineering  Laboratory,  CRREL  Report  (in 
prep.) 

Cole,  D.M.  and  W.F.  St.  Lawrence  (1984)  Acous¬ 
tic  emission  from  ice.  In  Third  International  Sym¬ 
posium  on  Acoustic  Emissions  and  Microseismic 
Activity  in  Geologic  Structures  and  Materials 
(H.R.  Hardy,  Jr.  and  F.W.  Leighton,  Ed.).  Penn¬ 
sylvania  State  University  Press. 

Cottrell,  A.H.  (1958)  Theory  of  brittle  fracture  in 
steel  and  similar  metals.  Transactions  of  the  Met¬ 
allurgical  Society  of  AIME,  April,  pp.  192-203. 
Cousland,  S.McK.  and  C.M.  Scala  (1981)  Acous¬ 
tic  emission  and  microstructure  in  aluminum 
alloys  7075  and  7050.  Metallurgical  Science,  15(1 1 
and  12):  609-614. 

Currier,  J.H.  (1983)  The  brittle  to  ductile  transi¬ 
tion  in  polycrystalline  ice  under  tension.  USA 
Cold  Regions  Research  and  Engineering  Labora¬ 
tory,  CRREL  Report  83-14. 

Dieter,  G.E.  (1976)  Mechanical  Metallurgy.  New 
York:  McGraw-Hill. 

Duval,  P.  and  H.  LeGac  (1980)  Does  the  perma¬ 
nent  creep-rate  of  polycrystalline  ice  increase  with 
crystal  size?  Journal  of  Geophysics,  25(91). 

Evans,  A.G.  (1982)  Acoustic  emission  sources  in 
brittle  solids.  In  Fundamentals  of  Acoustic  Emis¬ 
sions  (K.  Ono,  Ed.),  pp.  209-228. 

Frederking,  R.  (1977)  Plane-strain  compressive 
strength  of  columnar-grained  ice  and  granular- 
snow  ice.  Journal  of  Glaciology,  18(80):  505-516. 


49 


Gandhi,  C.  and  M.F.  Ashby  (1979)  Fracture 
mechanism  maps  for  materials  which  cleave: 
FCC,  BCC  and  HCP  metals  and  ceramics.  Acta 
Metallurgica,  27:  1565-1602. 

Gold,  L.W.  (1960)  The  cracking  activity  in  ice 
during  creep.  Canadian  Journal  of  Physics,  38(9): 
1137-1148. 

Gold,  L.W.  (1965a)  The  initial  creep  of  columnar¬ 
grained  ice.  Part  I.  Observed  behavior.  Canadian 
Journal  of  Physics,  43:  1414-1422. 

Gold,  L.W.  (1965b)  The  initial  creep  of  columnar¬ 
grained  ice.  Part  II.  Analysis.  Canadian  Journal 
of  Physics,  43:  1423-1434. 

Gold,  L.W.  (1966)  Elastic  and  strength  properties 
of  freshwater  ice.  Proceedings,  Ice  Pressure 
Against  Structures,  Laval  University,  Quebec,  pp. 
13-23. 

Gold,  L.W.  (1967)  Time  to  formation  of  first 
cracks  in  ice.  Proceedings,  International  Confer¬ 
ence  on  Low  Temperature  Science,  Sapporo, 
Japan.  Vol.  1,  Part  1,  pp.  359-370. 

Gold,  L.W.  (1970a)  Process  of  failure  in  ice.  Can¬ 
adian  Geotechnical  Journal,  7:  405-413. 

Gold,  L.W.  (1970b)  Failure  of  ice.  In  Proceed¬ 
ings,  IAHR  Ice  Symposium,  Reykjavik,  pp.  1-6. 
Gold,  L.W.  (1972)  The  process  of  failure  in  col¬ 
umnar-grained  ice.  Philosophical  Magazine, 
26(2):  311-328. 

Gold,  L.W.  (1977)  Engineering  properties  of 
freshwater  ice.  Journal  of  Glaciology,  19(81): 
197-212. 

Goodman,  D.J.  (1977)  Creep  and  fracture  of  ice 
and  surface  strain  measurements  on  glaciers  and 
sea  ice.  Ph.D.  thesis,  Christ’s  College,  Cam¬ 
bridge. 

Hirth,  J.P.  and  J.  Lothe  (1968)  Theory  of  Dislo¬ 
cations.  New  York:  McGraw-Hill. 

Hobbs,  P.V.  (1974)  Ice  Physics.  Cambridge:  Ox¬ 
ford  University  Press. 

Jacka,  T.H.  (1984)  The  time  and  strain  required 
for  minimum  ice  strain  rates.  Cold  Regions  Sci¬ 
ence  and  Technology,  8(3):  261-268. 

Jacka,  T.H.  and  M.  Maccagnan  (1984)  Ice  crystal¬ 
lographic  and  strain  rate  changes  with  strain  in 
compression  and  extension.  Cold  Regions  Science 
and  Technology,  8(3):  269-286. 

Jones,  S.J.  and  H.A.M.  Chew  (1983)  Effect  of 
sample  and  grain  size  on  the  compressive  strength 
of  ice.  Annals  of  Glaciology,  4:  129-132. 

Kamb,  W.B.  (1962)  Refraction  corrections  for 
universabstage  measurements.  I.  Uniaxial  crystals. 
American  Mineralogist,  47:  227-245. 


Khan,  M.A.,  T.  Shoji  and  T.  Takahashi  (1982) 

Acoustic  emission  from  cleavage  microcracking  in 
alloy  steels.  Metallurgical  Science,  16:  118-126. 
Langway,  C.C.  (1958)  Ice  fabric  and  the  universal 
stage.  USA  Snow,  Ice  and  Permafrost  Research 
Establishment  (SIPRE),  Technical  Report  62. 

Li,  J.C.M.  and  Y.T.  Chou  (1970)  The  role  of  dis¬ 
locations  in  the  flow  stress  grain  size  relationships. 
Metallurgical  Transactions,  1:  1145-1159. 

Lim,  P.N.  (1983)  The  effects  of  temperature  and 
grain  size  on  the  tensile  strength  of  ice.  M.S. 
thesis,  Thayer  School  of  Engineering,  Dartmouth 
College,  Hanover,  N.H. 

McMahon,  C.J.  and  M.  Cohen  &1965)  Initiation 
of  cleavage  in  polycrystalline  iron.  Acta  Metal¬ 
lurgica,  13(June):  591-604. 

Mellor,  M.  and  D.M.  Cole  (1982)  Deformation 
and  failure  of  ice  under  constant  stress  or  constant 
strain  rate.  Cold  Regions  Science  and  Technology, 
5:  201-219. 

Mendiralta,  M.G.,  S.M.L.  Sastry  and  J.V.  Smith 

(1976)  Effect  of  grain  size  upon  flow  and  fracture 
in  a  precipitation  strengthened  Ti-8  wt%  Al-0.25 
wt9/’o  Si  alloy.  Journal  of  Material  Science,  11: 
1835-1842. 

Ono,  K.,  R.  Landy  and  C.  Ouchi  (1978)  On  the 
amplitude  distribution  of  burst  emission  due  to 
MnS  inclusions  in  HSLA  steels.  Proceedings, 
Fourth  Acoustic  Emission  Symposium,  High 
Pressure  Institute  of  lapan,  pp.  4-33  to  4-44. 
Pollock,  A. A.  (1981)  Acoustic  emissions  ampli¬ 
tude  distributions.  International  Advances  in 
Nondestructive  Testing,  7:  215-239. 

St.  Lawrence,  W.F.  and  D.M.  Cole  (1982)  Acous¬ 
tic  emissions  from  polycrystalline  ice.  Cold  Re¬ 
gions  Science  and  Technology,  5:  183-199. 
Schulson,  E.M.  (1979)  An  analysis  of  the  brittle  to 
ductile  transition  in  polycrystalline  ice  under  ten¬ 
sion.  Cold  Regions  Science  and  Technology,  1: 
87-91. 

Scruby,  C.,  H.  Wadley  and  J.E.  Sinclair  (1981) 

The  origin  of  acoustic  emission  during  deforma¬ 
tion  of  an  aluminum-magnesium  alloy.  Philo¬ 
sophical  Magazine,  Series  A,  44(2):  249-274. 
Shewmon,  P.G.  (1969)  Transformations  in 
Metals.  New  York:  McGraw-Hill,  p.  54. 

Sinha,  N.K.  (1978)  Observation  of  basal  disloca¬ 
tions  in  ice  by  etching  and  replicating.  Journal  of 
Glaciology,  21(85):  385-395. 

Sinha,  N.K.  (1082)  Acoustic  emissions  and  micro- 
cracking  in  ice.  Proceedings  of  the  1982  Joint 
Conference  on  Experimental  Mechanics,  Oahu- 
Maui,  Hawaii,  pp.  767-772. 


Smith,  E.  and  J.T.  Barnby  (1967)  Crack  nuclea- 
tion  in  crystalline  solids.  Metal  Science  Journal,  1: 
56-64. 

Stroll,  A.N.  (1954)  The  formation  of  cracks  as  a 
result  of  plastic  flow.  Proceedings,  Royal  Society, 
A223:  404-414. 

Stroll,  A.N.  (1957)  A  theory  of  the  fracture  of 
metals.  Advances  in  Physics,  6:  418-465. 
Terlinde,  G.  and  G.L.  Luetjering  (1982)  Influence 
of  grain  size  and  age  hardening  on  dislocation 
pile-ups  and  tensile  fracture  for  a  Ti-Al  alloy. 
Metallurgical  Transactions,  A,  13A(July): 
1283-1292. 

Wadley,  H.N.G.,  C.B.  Scruby  and  G.S.  Shrimp- 
ton  (1981)  Quantiative  acoustic  emission  source 
characterization  during  low  temperature  cleavage 


and  intergranular  fracture.  Acta  Metallurgica,  29: 
399-414. 

Wang,  Y.S.  (1979)  Sea  ice  properties.  Exxon 
Technical  Seminar  on  Alaskan  Beaufort  Sea  Grav¬ 
el  island  Design.  Exxon,  Houston,  Texas. 
Zaretsky,  Y.K.,  A.M.  Fish,  V.P.  Gavrilo  and 
A.V.  Gusev  (1976)  Short-term  ice  creep  and  mi¬ 
crocrack  formation.  USA  Cold  Regions  Research 
and  Engineering  Laboratory,  Draft  Translation 
539,  pp.  196-202. 

Zaretsky,  Y.K.,  B.D.  Chumichev  and  V.I.  Sol- 
matin  (1979)  Ice  behavior  under  load.  Engineering 
Geology,  13:  299-309. 

Zener,  C.  (1948)  Fracturing  of  Metals.  American 
Society  of  Metals. 


10.00 


MICROFRACTURE  LENGTH  (mm) 


53 


MICROFRACTURE  LENGTH  (mm) 


& 

V/. 

y.v 

y* 


1 

\-‘1 


-  *  ^VA/iVf^y 


-  -V  A  - 


*-  A  A  -  ^ 


59 


MICROFRACTURE  LENGTH  (mm) 


rsvvs 


i  i  i  i  i  i  r 

o.oo  a. oo  4.oo  a. oo 


MICROFRACTURE  LENGTH 


i  r 

a. oo 
(mm) 


65 


6.00 


8.00 


10.00 


OF  MICROFRACTURES 


.00 


n  i  i  i - 1 - 1  i  i - r 

a. oo  4.oo  a. oo  a.oo 

MICROFRACTURE  LENGTH  (mm) 


— i 

10.00 


69 


APPENDIX  B:  CRYSTAL  ORIENTATIONS 


This  appendix  contains  pole  diagrams  for  two  specimens  containing  cracks.  For  each 
specimen,  a  number  of  measurements  were  taken  to  indicate  the  random  nature  of  the  grain 


A  facsimile  catalog  card  in  Library  of  Congress  MARC 
format  is  reproduced  below. 


Cole,  David  M. 

Effect  of  grain  size  on  the  internal  fracturing  of  poly¬ 
crystalline  ice  /  by  David  M.  Cole.  Hanover,  N.H.:  U.S. 
Army  Cold  Regions  Research  and  Engineering  Laboratory; 
Springfield,  Va.:  available  from  National  Technical  Informa¬ 
tion  Service,  1986. 

v,  79  p.,  illus.;  28  cm.  (  CRREL  Report  86-5.  ) 

Prepared  for  the  Office  of  the  Chief  of  Engineers  by 
Corps  of  Engineers,  U.S.  Army  Cold  Regions  Research  and 
Engineering  Laboratory  under  DA  Project  4A762730AT42. 
Bibliography:  p.  49. 

I.  Acoustic  emissions.  2.  Creep  tests.  3.  Fracture 
(mechanics).  4.  Grain  size.  5.  Ice.  6.  Polycrystalline. 

1.  United  States.  Army.  Corps  of  Engineers.  II.  Cold  Re¬ 
gions  Research  and  Engineering  Laboratory,  Hanover,  N.H. 
III.  Series:  CRREL  Report  86-5. 


dva  qovernment 


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